The traditional counting system used in the Welsh language is vigesimal, i.e. based on twenties where numbers from 11 to 14 are "x on ten", 16–19 are "x on fifteen" (though 18 is more usually "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 Welsh: tri deg pump (three ten five) while in vigesimal it is Welsh: pymtheg ar hugain (fifteen – itself "five-ten" – on twenty).
| Number | Vigesimal system | Decimal system | |
|---|---|---|---|
| 0 | Welsh: sero/dim | ||
| 1 | Welsh: un | ||
| 2 | Welsh: dau (m), Welsh: dwy (f) | ||
| 3 | Welsh: tri (m), Welsh: tair (f) | ||
| 4 | Welsh: pedwar (m), Welsh: pedair (f) | ||
| 5 | Welsh: pum(p) | ||
| 6 | Welsh: chwe(ch) | ||
| 7 | Welsh: saith | ||
| 8 | Welsh: wyth | ||
| 9 | Welsh: naw | ||
| 10 | Welsh: deg/un deg, Welsh: deng | ||
| 11 | Welsh: un ar ddeg ("one on ten") | Welsh: un deg un | |
| 12 | Welsh: deuddeg, Welsh: deuddeng | Welsh: un deg dau/dwy | |
| 13 | Welsh: tri/tair ar ddeg | Welsh: un deg tri/tair | |
| 14 | Welsh: pedwar/pedair ar ddeg | Welsh: un deg pedwar/pedair | |
| 15 | Welsh: pymtheg, Welsh: pymtheng | Welsh: un deg pump | |
| 16 | Welsh: un ar bymtheg ("one on fifteen") | Welsh: un deg chwech | |
| 17 | Welsh: dau/dwy ar bymtheg | Welsh: un deg saith | |
| 18 | Welsh: deunaw/tri/tair ar bymtheg ("two nines"/"three on fifteen") | Welsh: un deg wyth | |
| 19 | Welsh: pedwar/pedair ar bymtheg | Welsh: un deg naw | |
| 20 | Welsh: ugain | Welsh: dau ddeg | |
| 21 | Welsh: un ar hugain ("one on twenty") | Welsh: dau ddeg un | |
| 22 | Welsh: dau/dwy ar hugain | Welsh: dau ddeg dau/dwy | |
| 23 | Welsh: tri/tair ar hugain | Welsh: dau ddeg tri/tair | |
| 24 | Welsh: pedwar/pedair ar hugain | Welsh: dau ddeg pedwar/pedair | |
| 25 | Welsh: pump ar hugain | Welsh: dau ddeg pump | |
| 26 | Welsh: chwech ar hugain | Welsh: dau ddeg chwech | |
| 27 | Welsh: saith ar hugain | Welsh: dau ddeg saith | |
| 28 | Welsh: wyth ar hugain | Welsh: dau ddeg wyth | |
| 29 | Welsh: naw ar hugain | Welsh: dau ddeg naw | |
| 30 | Welsh: deg ar hugain ("ten on twenty") | Welsh: tri deg | |
| 31 | Welsh: un ar ddeg ar hugain | Welsh: tri deg un | |
| 32 | Welsh: deuddeg ar hugain | Welsh: tri deg dau/dwy | |
| etc. | |||
| 40 | Welsh: deugain ("two twenty") | Welsh: pedwar deg | |
| 41 | Welsh: deugain ac un ("two twenty and one") | Welsh: pedwar deg un | |
| 50 | Welsh: deg a deugain | Welsh: pum deg Welsh: hanner cant ("half a hundred") | |
| 51 | Welsh: un ar ddeg a deugain | Welsh: pum deg un Welsh: hanner cant ac un | |
| 60 | Welsh: trigain ("three twenty") | Welsh: chwe deg | |
| 61 | Welsh: trigain ac un | Welsh: chwe deg un | |
| 70 | Welsh: deg a thrigain ("ten and three twenty") | Welsh: saith deg | |
| 71 | Welsh: un ar ddeg a thrigain ("one on ten and three twenty") | Welsh: saith deg un | |
| 80 | Welsh: pedwar ugain ("four twenty") | Welsh: wyth deg | |
| 81 | Welsh: pedwar ugain ac un | Welsh: wyth deg un | |
| 90 | Welsh: deg a phedwar ugain ("ten and four twenty") | Welsh: naw deg | |
| 91 | Welsh: un ar ddeg a phedwar ugain ("one on ten and four twenty") | Welsh: naw deg un | |
| 100 | Welsh: can(t) | ||
| 200 | Welsh: dau gant | ||
| 300 | Welsh: tri chant | ||
| 400 | Welsh: pedwar cant | ||
| 500 | Welsh: pum cant | ||
| 600 | Welsh: chwe chant | ||
| 700 | Welsh: saith cant | ||
| 800 | Welsh: wyth cant | ||
| 900 | Welsh: naw cant | ||
| 1000 | Welsh: mil | ||
| 2000 | Welsh: dau fil/dwy fil | ||
| 1,000,000 | Welsh: miliwn | ||
| 1,000,000,000 | Welsh: biliwn | ||
| 1,000,000,000,000 | Welsh: 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" (Welsh: dau and Welsh: dwy), "three" (Welsh: tri and Welsh: tair) and "four" (Welsh: pedwar and Welsh: pedair), which must agree with the grammatical gender of the objects being counted. The numerals for "five", "six" and "hundred" (Welsh: pump, Welsh: chwech and Welsh: cant) also have reduced forms (Welsh: pum, Welsh: chwe, Welsh: can) when they precede the object they are counting. The words for "ten", "twelve", and "fifteen" (Welsh: deg, Welsh: un deg dau/deuddeg, Welsh: un deg pump/pymtheg) have the alternative forms Welsh: deng, Welsh: deuddeng, Welsh: 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).[2]
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 Welsh: 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 Welsh: mil naw chwe(ch) pump. This system appears to have broken down for years after 2000, e.g. whereas 1905 is Welsh: mil naw dim pump, 2005 is Welsh: 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.[3]
The singular form of the noun is used with numbers, but for larger numbers an alternative form is permitted, where Welsh: 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 Welsh: ar ("on") in the traditional system.
Nouns are also mutated following many numbers. Welsh: Un triggers the soft mutation (Welsh: treiglad meddal) of feminine nouns, other than those beginning with "ll" and "rh", but not masculine nouns. Welsh: Dau and Welsh: dwy both trigger the soft mutation (ll and rh included). Welsh: Tri (but not Welsh: tair) and Welsh: chwe trigger the aspirate mutation. Several higher numbers (Welsh: pum, Welsh: saith, Welsh: wyth, Welsh: deng, Welsh: deuddeng, and Welsh: pymtheng) trigger the nasal mutation when used with Welsh: blynedd ("year(s)"). The part of the number immediately preceding the noun will determine any mutation of the noun. In the plural form with Welsh: o, the soft mutation is used as is normal after Welsh: o.
The following example illustrates several of these points: