An Caighdeán Oifigiúil: Chapter 9: Numbers (pp. 141-170)

9.1 General

9.1.1 The primary forms of numbers in Irish are Standalone Numbers, Cardinal Numbers, Personal Numbers, Ordinal Numbers, Fractions and Decimals.

(a) Standalone Numbers

Numbers without a noun directly following them are called Standalone Numbers. They are used in simple counting, e.g. a haon; a cúig; a deich (see 9.2).

(b) Cardinal Numbers

Numbers placed before nouns to convey the amount of something are called Cardinal Numbers, e.g. trí leabhar; seacht gcupán; naoi mbád (see 9.3).

(c) Personal Numbers

Numbers used to count people are called personal numbers, e.g. beirt bhan; ceathrar daltaí; ochtar feirmeoirí (see 9.4).

(d) Ordinal Numbers

Ordinal numbers are those used to convey the place of something in a series, e.g. an chéad teach; an dara bean; an fichiú haois (see 9.5).

(e) Fractions

Fractions are numerical quantities that are not integers (whole numbers), e.g. ceathrú (1/4); ceithre chúigiú (4/5); cúig shéú (5/6) (see 9.6).

(f) Decimals

Decimals are another way of conveying a numerical quantity that is not an integer, using the decimal point, e.g. 3.1; 7.5; 18.49; 34.023 (see 9.7).

9.1.2 A choice can be made between two systems for dealing with ordinal numbers and personal numbers in writing: the Established System and the Simplified System. The Established System is always used for the numbers 1 – 19. Either the Established System or the Simplified System can be used for the numbers 20 and onwards.

9.2 Standalone Numbers

Standalone numbers are those that are used in simple counting when not conveying a meaning of an amount or oder of things or people, e.g. a haon; a trí déag; a tríocha trí; céad nócha a cúig; míle, ceithre chéad seachtó a naoi.

9.2.1 Standalone Numbers 0 – 99

(a) The particle a is placed before the numbers 1 – 19, e.g. a haon; a dó; a trí; bus a ceathair; a hocht déag; and in the case of the numbers 20 – 99 (apart from the tens), it is placed before the final number, e.g. fiche a haon; daichead a sé; seachtó a hocht.

(b) An equal status is given to the words ceathracha and daichead.

The standalone numbers 0 – 19 are written as follows:

Note that the standalone numbers are used in matters of time, e.g. a haon a chlog; a seacht a chlog; a fiche tar éis a cúig. Time is also written in figures as: 5.30 p.m.; 4.26 p.m.; 13:00; 16:47.

The standalone numbers 20 – 99 are written as follows. The whole system is given between 20 and 29 in the table and then examples are given in every other instance.

9.2.2 Standalone Numbers 100+

(a) The numbers céad, míle, miliún, biliún, etc. are nouns. Therefore, the basic number system is used if the numbers 2 – 19 appear before a string of zeroes corresponding to céad, míle, miliún, biliún, etc., e.g. ceithre chéad; dhá chéad míle; naoi miliún déag; dhá bhiliún; ocht mbiliún (see 9.3 Ordinal Numbers).

(b) No initial mutations are made to nouns following tens, e.g. fiche míle; tríocha miliún; etc.

9.2.3 Standalone Numbers 10,000+

(a) There are two systems for expressing numbers above 10,000 – the cardinal number system and the standalone number system.

(b) In the cardinal number system, the word order follows the rules for cardinal numbers, e.g. 24,000 – ceithre mhíle is fiche (see Table 9N). In the standalone number system, the standalone number is used with the magnitude (céad, míle, etc.) without any transformation, e.g. 24,000 – fiche a ceathair míle.

Note that is is used in the cardinal number system above 10,000 but it is not used with other standalone numbers.

The standalone numbers above 10,000 are written as follows.

9.3 Cardinal Numbers

9.3.1 Cardinal Numbers 1 – 19

(a) Numbers used with a noun to express the amount of something are called cardinal numbers.

(b) The noun follows aon, dhá, trí, ceithre, cúig, sé, seacht, ocht, naoi, deich.

(c) Note that the cardinal numbers dhá and ceithre are used instead of the standalone forms dó and ceathair.

(d) The word amháin must be mentioned after the cardinal number aon and the noun. It is not, however, necessary for aon to be used always, e.g. aon chapall amháin; capall amháin.

(e) No lenition is caused to d, t or s after aon, e.g. aon doras amháin; aon teach amháin.

(f) The word déag comes after the noun, e.g. ceithre leabhar déag. The word déag is lenited if the word directly before it ends in a vowel (but see 9.3.2(e)), except after euro.

Note that if a noun and a qualifier form a single unit of meaning, e.g. madra rua; cat crainn; teach tábhairne; láthair champála (as opposed to a simple noun and a qualifier, e.g. leabhar dearg), the word déag is placed after both the noun and the qualifier, e.g. ceithre mhadra rua dhéag; cúig theach tábhairne dhéag; sé chat crainn déag; seacht n-iora ghlasa dhéag. Any other qualifiers are added after déag, e.g. sé chat crainn déag mhóra; seacht n-iora ghlasa dhéag fhiáine.

(g) No lenition is caused to dhá after the article, aon or céad, e.g. an dá leabhar; an chéad dá leabhar; aon dá leabhar.

(h) The cardinal numbers aon, dhá (but see 8.3.3), trí, ceithre, cúig and sé lenite the singular noun that follow them, e.g. trí bhád; but they do not lenite the word cent, e.g. trí cent.

(i) The cardinal numbers seacht, ocht, naoi and deich eclipse the singular and plural nouns that follow them, e.g. seacht gcnámh; deich gcinn; but they do not eclipse the word euro, e.g. ocht euro; naoi euro, or cent, e.g. ocht cent, deich cent.

9.3.2 Nouns that have a special plural form following cardinal numbers

There are some nouns for which the nominative plural form, or a special plural form, is used after the cardinal numbers 3 – 10 and after numbers that end in 3 – 9. Those nouns are highlighted in the table below. Although fichid is not a plural form, it is included in this class.

(a) The nominative singular of a noun is used with the cardinal numbers 1 – 2 and after numbers ending in 1 – 2, e.g. aon phingin amháin; dhá bhliain; aon uair déag; dhá cheann is tríocha.

(b) No lenition is caused to the plural form after 3 – 6 nor numbers ending in 3 – 6, e.g. trí seachtaine; ceithre cinn déag.

(c) After 3 – 6 and numbers ending in 3 – 6 an h is added to the plural form uaire, e.g. cúig huaire.

(d) The numbers 7 – 10 and numbers ending in 7 – 10 eclipse the plural form, e.g. seacht mbliana; ocht bpingine déag.

(e) The word déag is not lenited after the plural forms, even if they end in a vowel, e.g. trí bliana déag; ocht n-uaire déag.

(f) The nominative singular is used after the tens (except deich), e.g. fiche bliain; tríocha pingin; ochtó troigh.

9.3.3 Adjectives with Cardinal Numbers 1 – 19

(a) After the cardinal number 1, adjectives accompanying the noun are in the singular and the same gender as the noun.

(b) After the other numbers (2 – 19), the adjective is in the plural and is lenited.

(c) The word déag is placed before any adjective(s) that accompany the noun (but see 9.3.1(f)).

9.3.4 Adjective form with nouns that have a special plural form

(a) After the cardinal number 1, adjectives accompanying a noun are in the singular, and the same gender as the noun.

(b) The adjective is put in the plural after the plural forms, but is not lenited if the plural form ends in a vowel. The adjective is lenited after cinn and fichid.

9.3.5 The Article with Cardinal Numbers 1 – 19

(a) Singular form of the article

(i) The singular form of the article is used before the cardinal number 1, numbers ending in 1 and before plurals of tens from twenty onwards.

(ii) After the article, t- is placed before the cardinal number aon, e.g. an t-aon leabhar amháin; an t-aon bhileog amháin. The t- is dropped after a preposition, e.g. san aon leabhar amháin; tríd an aon fhuinneog amháin.

(iii) The singular form of the article is also used before the cardinal number dhá, but it becomes dá, e.g. an dá chapall.

(b) Plural form of the article

(i) The plural form of the article is placed before the cardinal numbers 3 – 9 and 13 – 19.

(ii) After the plural form of the article, h is added to cardinal numbers starting with a vowel, e.g. na hocht gcapall.

(c) The article does not make any change to adjectives following cardinal numbers and a noun, e.g. an dá chapall mhóra.

Note: Note that for nouns having a special plural form after cardinal numbers, they follow the same pattern, e.g. an t-aon bhliain amháin; an dá cheann mhóra; na hocht dtroithe déag, etc.

9.3.6 Cardinal Numbers 1 – 19 – the Genitive without the Article

(a) Both nouns and adjectives change their form in the genitive after aon, e.g. ualach aon chapaill mhóir amháin; fráma aon fhuinneoige báine amháin; except when accompanied by déag, e.g. ualach aon chapall déag mhóra; fráma aon fhuinneog déag bhána.

(b) In the case of 2 – 19, no form changes are made to the noun or the cardinal number, e.g. fad dhá mhéadar; costas trí fhuinneog; úinéir seacht ngabhar; tréimhse naoi n-oíche; tiománaithe trí thacsaí dhéag; but the adjective is put in the plural and is lenited, e.g. costas trí fhuinneog dheasa; úinéir seacht ngabhar chrosta; tiománaithe trí thacsaí dhéag chostasacha; except if there is a special plural form that ends in a vowel or broad consonant, e.g. trí bliana crua.

9.3.7 Cardinal Numbers 1 – 19 – the Genitive with the Article

(a) aon

Both nouns and adjectives change their form in the genitive after aon when the article is present according to the following points.

(i) According to the gender of the noun, an or na is used in the genitive before the cardinal number aon when not accompanied by déag, e.g. ualach an aon chapaill amháin; costas na haon fhuinneoige amháin; but ábhar an aon chuntas déag amháin; ag ceartú an aon aiste dhéag shuimiúla.

(ii) If the noun is feminine, an h must be added to the start of the cardinal number aon, e.g. i gcaitheamh na haon oíche amháin.

(iii) If the noun is masculine, the t- before the cardinal number aon is removed, e.g. ar feadh an aon lae amháin sin.

(b) After the singular article (an, don, sa, etc.) dhá becomes dá.

(c) After the article in the genitive (na), the cardinal numbers trí to deich admitting eclipsis are eclipsed (trí, ceithre, cúig, ocht, deich).

(d) The same rules come into effect for nouns having a special plural form and the adjectives accompanying them (see 9.3.4) that are in effect in the nominative case, e.g. tréimhse na sé bliana fada; deireadh na naoi seachtaine déag fada; Cogadh na Naoi mBliana; costas na dtrí troithe cearnacha eile; úinéir an dá cheann bhána; praghas na dtrí cinn mhóra.

9.3.8 Writing the cardinal numbers 1 – 19 in figures

The same rules apply for writing the cardinal numbers 1 – 19 in figures as apply for writing them in words, e.g. 1 chapall mór; 3 bhád bheaga; 7 n-oíche dhorcha; 13 seachtaine fuara; 17 ngluaisteán shaora; 19 mbliana fada.

9.3.9 Cardinal Numbers 20+ – Tens

(a) The nominative singular form of the noun is used after multiples of ten. No initial mutation is made to the noun.

(b) If an adjective is present, it agrees with the gender of the noun.

(c) The singular form of the article is used before tens, e.g. an fiche teach nua; an seasca duine cáiliúil.

(d) In the genitive case, if the article is not present, neither the noun nor the cardinal number undergo any change of form.

(e) If the article is present in the genitive case, it affects the initial letter of the number as it would a masculine noun, but no initial mutation is made to f or s.

Note: When a plural form of a multiple of ten is used, the noun following it is in the genitive plural, e.g. na céadta daoine; na mílte dathanna.

The genitive plural also follows the singular nouns dosaen and scór, e.g. dosaen amhrán; scór daoine.

9.3.10 Other Cardinal Numbers 20+

(a) There exist two systems for numbers above 20 (except the tens, see 9.3.9): the Established System and the Simplified System. These two systems apply to cardinal numbers written both in words and figures. Both of these systems have equal status and are acceptable.

(b) The Established System

(i) The noun is in either its singular form or its special plural form and initial mutations are made as is appropriate to the noun.

(ii) After numbers ending in 1, adjectives agree with the gender of the noun. For numbers ending in 2 – 9, the adjective is in the plural and is lenited (but see 9.3.4).

(c) The Simplified System

(i) The noun is always in the singular, even if it has a special plural form, and no initial mutations are made. The adjective is always in the singular and it is lenited according to the gender of the noun.

(ii) For numbers ending in 2 or 4, the standalone forms dó and ceathair are used instead of dhá and ceithre.

(d) For multiples of 10 there is only one form, e.g. céad is fiche bád.

(e) With regards to the article, the same pattern is followed as the cardinal numbers 1 – 19 for the cardinal numbers above 20, e.g. an t-aon leabhar is fiche; an dá bhord is tríocha; na cúig pheann is seasca (see 9.3.5).

Note: When an adjective accompanies a cardinal number, it is possible to use the plural form of the noun ceann (cinn) followed by the preposition de, e.g. seacht gcinn déag d’oícheanta ciúine; trí cinn is tríocha de bháid mhóra.

Another option is to use the standalone number, the preposition de and the plural form of the noun and adjective accompanying it, e.g. a haon déag de bhlianta fada; tríocha a trí de bháid mhóra.

9.3.11 Cardinal Numbers 100+

In the Established System, the alternative syntax used for numbers below 100 is also used with numbers above 100, e.g. céad fiche is aon chapall amháin; dhá mhíle; trí chéad is ceithre chapall; etc.

The other rules are the same as the rules for cardinal numbers explained in 9.3.10.

9.3.12 Writing Cardinal Numbers 20+ in Figures

When cardinal numbers above 20 are written in figures, the rules of the Established System and the Simplified System apply respectively.

9.4 Personal Numbers

Numbers that express an amount of people are called personal numbers.

9.4.1 Use of Personal Numbers

(a) The personal numbers (2 – 10 and 12) are used to count people.

(b) The normal system of cardinal numbers is used to express ‘eleven people’ or numbers of people more than twelve, e.g. aon duine dhéag; trí dhuine dhéag; ceithre dhuine is daichead.

9.4.2 Bare Use of Personal Numbers

(a) Bare personal numbers

(i) It is possible to use a personal number ‘bare’ (without a noun following it) to count a number of people, e.g. An bhfaca tú an bheirt?; Gabhadh seachtar.

(ii) Bare personal numbers in the genitive are treated as regular nouns, e.g. cor beirte; col ceathrair; col seisir…

(b) The article before bare personal numbers

(i) All personal numbers are masculine except for beirt, e.g. an bheirt; an ceathrar; an t-ochtar.

(ii) After the article, aon or céad, dháréag is not lenited, e.g. bhí an dáréag ann; gach aon dáréag acu; an chéad dáréag a cháiligh.

(iii) When the article precedes them, bare personal numbers in the genitive are treated as regular nouns, e.g. cótaí an tseisir; ticéid an ochtair; gluaisteán na beirte.

(c) Adjectives with bare personal numbers – beirt

(i) If an adjective qualifies the word beirt when it is in the nominative (or vocative, dative or accusative), the adjective is lenited and is in the nominative plural, e.g. an bheirt cháiliúla; beirt mhisniúla; don bheirt óga.

(ii) If beirt is in the genitive and follows the article, then an adjective following it is in the feminine genitive singular, e.g. tuairimí na beirte díograisí; nótaí na beirte misniúla; iarrachtaí na beirte cróga.

(iii) If beirt is in the genitive but without the article, then an adjective following it which is referring to a preceding noun is in the plural after beirt and is lenited (and no genitive change is made to beirt but it is lenited), e.g. moltaí bheirt mhisniúla; tuairimí bheirt cháiliúla; obair bheirt acadúla.

(iv) If beirt, in the genitive and without the article, is qualified by a subsequent adjective that is subject to a compound preposition or verbal noun, then the adjective is in the plural after beirt and is lenited (and no change is made to beirt either), e.g. le haghaidh beirt inniúla; ag moladh beirt mhaithe.

(d) Adjectives with personal numbers – triúr to dháréag

(i) If the personal numbers triúr to dháréag (but see 9.4.1(b)) in the nominative (or vocative, dative or accusative) are qualified by a subsequent adjective, the adjective is in the nominative singular without any lenition, e.g. triúr mór; ceathrar ard; an cúigear saibhir; don dáréag clúiteach.

(ii) If the personal numbers triúr to dháréag (but see 9.4.1(b)) in the genitive are qualified by a subsequent adjective, the usual rules for adjectives following a noun in the genitive apply, e.g. éadaí an cheathrair bhig; meitheal ochtair dhíograisigh; airgead an dáréag chlúitigh (see Chapter 4).

9.4.3 Nouns with Personal Numbers

(a) Form of personal numbers and nouns following them

(i) If the word beirt in the nominative (or vocative, accusative or dative) is qualified by a subsequent noun, that noun is in the genitive plural and is lenited (except for nouns beginning with d, t or s), e.g. beirt chaptaen; beirt chumadóirí; beirt drumadóirí; ag beirt bhan.

(ii) If the word beirt, in the genitive and without the article, is qualified by a subsequent noun, which follows and is subordinate to another noun, no genitive change is made to beirt but it is lenited and the noun is in the genitive plural and is lenited (except nouns beginning with d, t or s), e.g. moltaí bheirt chumadóirí; tuairimí bheirt chaptaen; obair bheirt saineolaithe.

(iii) If the word beirt, in the genitive and without the article, is qualified by a subsequent noun, which follows and is subject to a compound preposition or verbal noun, no change is made to beirt and the noun is in the genitive plural and is lenited (except for nouns beginning with d, t or s), e.g. le haghaidh beirt mholtóirí; ag moladh beirt saighdiúirí.

(iv) The genitive plural of a noun follows the personal numbers triúr to dháréag (but see 9.4.1(b)) when people are being counted, e.g. triúr bádóirí; ceathrar múinteoirí.

(v) No genitive change is made to personal numbers triúr to dháréag (but see 9.4.1(b)) if a noun follows, e.g. athair ceathrar mac; máthair cúigear iníonacha; geansaithe dháréag peileadóirí.

* Note that 11 is treated as in the cardinal number system, and the noun is not in the genitive (see 9.3.6(a)).

(b) The article before personal numbers with a noun following them

(i) The singular form of the article is used before personal numbers. They are all masculine with the exception of beirt.

(ii) The words dháréag, aon and céad are not lenited following the article, e.g. an Dáréag Aspal; gach aon dáréag scoláirí; an chéad dáréag múinteoirí a cháiligh.

(iii) If the word beirt, in the genitive after the article, is qualified by a subsequent noun, the noun is in the genitive plural and is not lenited (but beirt undergoes genitive changes), e.g. tuairimí na beirte múinteoirí; nótaí na beirte saineolaithe; tuairiscí na beirte comhfhreagraithe; tithe na beirte deartháireacha.

(iv) No genitive change is made to the personal numbers triúr to dháréag, nor to nouns following them, but the article affects the first letter of the personal number as it would the genitive singular of any other noun, e.g. cótaí an cheathrar daltaí; oifig an tseachtar tréidlianna; Scoil an tSeachtar Laoch.

* Note that 11 is treated as in the cardinal number system, and the noun is not in the genitive (see 9.3.7(a)(i)).

(c) Adjectives with nouns following personal numbers

(i) Following the personal number beirt, adjectives are in the nominative plural and are lenited, e.g. beirt bhan cháiliúla; beirt ghirseach cruthaitheacha; beirt amhránaithe cháiliúla; beirt mhúinteoirí shealadacha.

(ii) If the word beirt, in the genitive and without the article preceding it, is qualified by a subsequent ‘noun + adjective’, following and subject to another noun, the adjective is in the plural and is lenited, e.g. moltaí bheirt léachtóirí acadúla; tuairimí bheirt iriseoirí sheanbhunaithe; saothar bheirt ghramadóirí chliste.

(iii) If the word beirt, in the genitive and without the article preceding it, is qualified by a subsequent ‘noun + adjective’, following and subject to a compound preposition or verbal noun, the adjective is in the plural and is lenited, e.g. le haghaidh beirt mholtóirí dheasa; ag moladh beirt chumadóirí shamhlaíocha.

(iv) Following the personal numbers triúr to dháréag (but see 9.4.1(b)), an accompanying adjective is in the genitive plural, e.g. triúr scoláirí díograiseacha; ceathrar girseach éirimiúil; bád an triúr bádóirí tuirseacha; airgeadais an deichniúr ban bríomhar. Examples with and without the article are given in the table below.

* Note that 11 is treated as in the cardinal number system, and the noun is not in the genitive (see 9.3.6(a) and 9.3.7(a)(i)).

9.4.4 Writing Personal Numbers in Figures

(a) It is recommended to write the personal numbers 1 – 12 in words rather than figures. If they are written in figures, they are treated as cardinal numbers, e.g. 2 bhean bheaga, 4 bhádóir cháiliúla, 7 bhfeirmeoir shaibhre (see 9.3.8).

(b) The cardinal number system is used to count people above twelve. See 9.3.1 for a description of the cardinal number system 1 – 19, e.g. trí bhean déag; ceithre ghirseach déag ghalánta; 17 mbádóir; 19 bhfear ocracha; and see 9.3.10 for a description of the cardinal number system above 20, e.g. trí bhean arda is caoga; 49 ngirseach ghalánta.

9.4.5 Personal Numbers – The Simplified System

It is possible to use a simplified number system with the cardinal and personal number systems above twenty. See 9.3.10(c) for a description of this Simplified System, e.g. fiche a cúig fear mór; tríocha a sé bean shaibhir; 46 bádóir cumasach; 56 girseach chróga.

9.5 Ordinal Numbers

Ordinal numbers are used to express the place of something in a series.

9.5.1 Ordinal Number 1

(a) It is possible to use the ordinal number céad (an chéad) with a singular or plural noun. The singular article is used when it is followed by a singular noun, e.g. an chéad chaibidil, and the plural article when it is followed by a plural noun, e.g. na chéad chaibidlí.

(b) The ordinal number céad is lenited after the article, e.g. an chéad leabhar; na chéad rialacha; but not:

(i) in the instances described in Chapter 1 when eclipsis follows the article in the dative case, e.g. ar an gcéad duine; leis an gcéad cheadúnas;

(ii) when céad is used as a prefix in a masculine or plural noun, e.g. céadainm, an céadainm; Céad-Aire, an Céad-Aire; céadonóracha; na céadonóracha; (but céadghairm, an chéadghairm; céadsearc, an chéadsearc; according to the usual rules for feminine nouns); or as a prefix in a verb, e.g. céadbhlaisim, céadbhlaisfidh sé (but ón uair a chéadbhlais mé é, according to the usual rules for verbs in the present tense indicative mood);

(iii) following the possessive adjectives a (feminine, third person singular), e.g. a céad cheolchoirm, and ár, bhur, a (third person plural), e.g. ár gcéad teach; bhur gcéad charr; a gcéad mhac.

(c) The ordinal number céad lenites the noun or adjective following it in every case, e.g. an chéad fhear; an chéad bhean; na chéad cheithre ghloine; na chéad bhlianta; clann an chéad fhir; mac na chéad mhná; lucht na chéad bhliana; if it does not begin with d, t, or s, e.g. na chéad daoine; an chéad saighdiúir; an chéad turas; ceadúnas an chéad tógálaí. (See 9.5.4 for more information on ordinal numbers in the genitive case.)

(d) The ordinal number céad is used in the place of 1, but for other ordinal numbers ending in 1, the word aonú is used. In the nominative case, after the article, t- is added to the start of aonú, e.g. an t-aonú lá is tríocha.

9.5.2 Ordinal Numbers 1 – 100 – General Information

(a) The singular form of the article is used before ordinal numbers (except for 1, see 9.5.1), e.g. an dara bean; an dóú teach; an tríú tuarascáil; an ceathrú bean is fiche; an cúigiú comhartha is seasca.

(b) After the ordinal number dara and all ordinal numbers ending in -ú, h is placed before a noun starting with a vowel, e.g. an dara hoíche; an tríú hurlár; an séú hóstán déag; an t-ochtú hurlár is tríocha.

(c) The article usually precedes the first number in the ordinal number, if there is no possessive adjective or gach before it, e.g. an tríú lá but gach dara bliain; a tríú bliain.

(d) A system following the same syntax as the cardinal numbers (Established System) is used to express the position of something in a series under 100, e.g. an dara hábhar is tríocha; an ceathrú cathaoir is caoga; an seachtú hoíche is seachtó; an t-ochtú madra is nócha.

(e) The word déag is not lenited in an ordinal number, e.g. an tríú duine déag; an t-ochtú bosca déag; an naoú leabhar déag.

9.5.3 Ordinal Numbers 100+

(a) A system based on the standalone number system is used for expressing the place of something in a series above 100, e.g. céad a ceathair – an céad is ceathrú feirmeoir; cúig chéad seasca a ceathair – an cúig chéad seasca is ceathrú heitleán; seacht míle, ceithre chéad a naoi déag – an seacht míle, ceithre chéad is naoú hóstán déag.

(b) The word déag is lenited after the number míle, e.g. an trí mhíle dhéag is ceathrú hoileán.

9.5.4 Ordinal Numbers in the Genitive Case

(a) For the ordinal number céad, the subsequent noun is declined and the article complies with the number and gender of the noun, e.g. an chéad fhear, clann an chéad fhir; an chéad bhean, clann na chéad mhná; na chéad cheithre bliana; na chéad chúig charr, plátaí clárúcháin na chéad chúig charr; na chéad taisceálaithe, eachtraí na chéad taisceálaithe.

(b) For all other ordinal numbers, the noun is not declined at all, e.g. mac an dara bean; mac an dara far; eagraíocht tríú tír; oideachas tríú leibhéal; clúdach an cheathrú tuarascáil; deireadh an fichiú haois; tús an aonú haois is fiche.

(c) The t- is dropped from aonú, ochtú, ochtódú, etc., e.g. an t-aonú bliain déag, tús an aonú bliain déag; an t-ochtú haois déag, tús an ochtú haois déag; an t-ochtódú cruinniú, miontuairiscí an ochtódú cruinniú.

(d) The article affects the ordinal number as it would a masculine noun, e.g. bróga an chúigiú girseach; seoladh an cheathrú teach is daichead; but no initial mutation is made to f nor s, e.g. lucht an seachtú hoifig; bonn an fichiú himreoir; deireadh an seascadú comhdháil.

9.5.5 Adjectives with Ordinal Numbers

Adjectives are declined in accordance with the noun, e.g. an chéad bhean mhór; an chéad fhear mór; seol an chéad bháid ghoirm; deireadh na chéad tuarascála cuimsithí; na chéad scoláirí maithe; eachtraí na chéad taisceálaithe cáiliúla; an tríú fear mór is tríocha; cóta an daicheadú bean mhór.

9.5.6 Writing Ordinal Numbers in Figures

(a) Ordinal numbers are written in figures by putting ú after the number, e.g. an 1ú, an 2ú, an 19ú, an 123ú.

(b) The rules relating to writing ordinal numbers in figures are the same as the rules for writing them in words (see 9.5.1 to 9.5.5 above). Note that h is placed before vowels and no lenition follows 1ú because it refers to aonú rather than céad.

9.6 Fractions

Fractions are numerical quantities that are not integers, e.g. 1/4 – ceathrú; 2/3 – dhá thrian; 5/6 – cúig shéú.

9.6.1 Composition of Fractions

(a) There are two parts to a simple fraction: the numerator and the denominator. The numerator is placed above the line and the denominator below the line, e.g. for 6/7, the numerator is 6 and the denominator is 7.

(b) Ordinal numbers are utilised to express the denominator, except in the instances of the words leath and trian.

Note that the special plural form treana of the noun trian is used following the numbers 3 – 10. This noun is left bare after trí, ceithre, cúig, sé, e.g. 3/3 – trí treana; 4/3 – ceithre treana; and it is eclipsed after seacht, ocht, naoi, deich, e.g. 9/3 – naoi dtreana; 10/3 – deich dtreana.

(c) When the numbers 11 – 19 are the denominator, a version derived from the ordinal number is used, e.g. 4/13 – ceithre thrídéagú; 6/15 – sé chúigdéagú.

(d) When a number above 20 is the denominator, the word order is the same as in standalone numbers, except that the ordinal number rather than the standalone number is placed at the end, e.g. 1/30 – tríochadú; 4/97 – ceithre nócha seachtú.

(e) Fractions are written in a few distinct ways, as explained below. Option (i) is the most commonly used structure.

(i) Standalone numbers can be used with the preposition ar or the compound preposition os cionn between them to express a fraction, e.g. 1/11 – a haon ar a haon déag; a haon os cionn a haon déag; 7/8 – a seacht ar a hocht; a seacht os cionn a hocht; 4/15 – a ceathair ar a cúig déag; a ceathair os cionn a cúig déag; 33/57 – tríocha a trí ar chaoga a seacht; tríocha a trí os cionn caoga a seacht; 136/82 – céad tríocha a sé ar ochtó dó; céad tríocha a sé os cionn ochtó dó. The word fiche is not lenited in fractions, e.g. 3/24 – a trí ar fiche a ceathair.

(ii) If the numerator is 1, the word cuid can be used with ordinal numbers to express fractions, e.g. 1/2 – leath; an leathchuid; 1/3 – trian; an tríú cuid; 1/11 – aondéagú; an t-aondéagú cuid. The form with cuid is usually used when the denominator is above 20, e.g. 1/27 – an fiche seachtú cuid; 1/156 – an céad caoga séú cuid. For the tens, however, one would sooner say tríochadú, etc. than an tríochadú cuid.

(iii) If the numerator is between 2 and 10, the cardinal numbers and the ordinal number form (see (b), (c) and (d) above) to express a fraction. The fractions are simple nouns and follow the usual rules for cardinal numbers when counting them, e.g. 7/8 – seacht gcinn d’ochtuithe; 4/15 – ceithre cinn de chúigdéaguithe;

(iv) If the numerator is more than 10, it is possible to use the standalone numbers as follows: numerator (as a standalone number) + de + plural of the denominator, e.g. 33/57 – tríocha a trí de chaoga seachtuithe; 136/82 – céad tríocha a sé d’ochtó dóithe. This form is best used when the numerator is above 10 and the denominator is above 20.

9.6.2 Denominators

(a) Denominators 2 – 19

The table below shows two options for writing fractions in which the denominator is between 2 – 19 and the numerator is 1.

(b) Denominators 20+

Examples are given in the table below of the way to deal with denominators above 20 (apart from tens) when the numerator is 1. It is common to use the version with cuid in the case of such fractions. The composition of this version is the same as the composition used in standalone numbers, except that an ordinal number is used at the end in place of a standalone number and that the numerical particle a is dropped.

Note that it is the ordinal number that is used for tens, e.g. fichiú, céadú, míliú, etc. and it is not common to use the version with cuid for them, e.g. 1/30 – tríochadú; 1/50 – caogadú.

9.6.3 Numerators

(a) Numerators 2 – 10

(i) The cardinal number system is followed when the numerator is more than 1 because the denominators are simple nouns (exception: fichiú is not lenited, e.g. trí fichiú). Examples are given in the table below of fractions for which the numerator is between 2 and 10.

(ii) In preference to this, it is possible to use the noun ceann/cinn along with the preposition de and the plural form of the denominator.

(b) Fractions where the Numerator is more than 10

When the numerator is more than 10, the standalone numbers are used as follows: numerator (as a standalone number) + de + plural of the denominator.

9.6.4 Large Numerators and Denominators

When the numerator is more than 10 and the denominator is more than 20, it is preferable to use the version with the standalone number + de + plural of the denominator. It is also possible to make use of two standalone numbers and the preposition ar or the compound preposition os cionn between them to express a fraction, e.g. 61/66 – seasca a haon ar sheasca a sé; seasca a haon os cionn seasca a sé; 74/83 – seachtó a ceathair ar ochtó a trí; seachtó a ceathair os cionn ochtó a trí; 437/500,043 – ceithre chéad tríocha a seacht ar chúig chéad míle daichead a trí; ceithre chéad tríocha a seacht os cionn cúig chéad míle daichead a trí.

9.7 Decimals

(a) The standalone number system is used for decimals, e.g. 1.7 – a haon ponc a seacht; 22.4 – fiche a dó ponc a ceathair; 84.22 – ochtó a ceathair ponc a dó.

(b) No inflection nor initial mutation is made to a noun following a decimal, whether in word or figure form, e.g. a haon ponc a dó gram; 1.5 cileagram; 7.4 méadar ciúbach.

9.8 Summary of Numbers

Note that:

(a) the Established System only is used for numbers under 20;

(b) it is recommended, for prose, to write personal numbers up to dháréag in words rather than figures.