primero - first
segundo - second
tercero - third
cuarto - fourth
quinto - fifth
sexto - sixth
séptimo - seventh
octavo - eighth
noveno or nono - ninth
décimo - tenth
undécimo - eleventh
duodécimo - twelfth
decimotercio or decimotercero - thirteenth
decimocuarto - fourteenth
decimoquinto - fifteenth
decimosexto - sixteenth
decimoséptimo - seventeenth
decimoctavo - eighteenth
decimonoveno or decimomono - ninteenth
vigésimo - twentieth
vigésimo prim(er)o - twenty-first
vigésimo segundo - twenty-second
trigésimo - thirtieth
cuadragésimo - fortieth
quincuagésimo - fiftieth
sexagésimo - sixtieth
septuagésimo - seventieth
octogésimo - eightieth
nonagésimo - ninetieth
centésimo - hundreth
centésimo prim(er)o - hundreth and first
centésimo segundo - hundreth and second
ducentésimo - two hundreth
tricentésimo - three hundreth
cuadringentésimo - four hundreth
quingentésimo - five hundreth
sexcentésimo - six hundreth
septingentésimo - seven hundreth
octingentésimo - eight hundreth
noningentésimo - nine hundreth
miléimo - thousandth
dos milésimo - two thousandth
doscientos milésimo - two hundred thousandth
millonésimo - millionth
dos millonésimo - two millionth

Things to note:
In most cases you can use the cardinal number in place of the ordinal numbers above tenth (décimo).

The ordinals primero (first) and tercero (third) drop the final "o" before a masculine singular noun.

el primer presidente      -     the first president
el tercer ejemplar         -      the third copy

The numbers can be abbreviated by using the last syllable or the last letter of the number to the written number.  The ending must agree with the gender of the noun.

El 1ro hombre             - the first (or 1st) man
El 1o hombre             - the first (or 1st) man
La 2da lección            - the second (or 2nd) lesson
La 2a lección             - the second (or 2nd) lesson

Note that lesson is "la lección".  As such the word for second would be segunda not segundo.

Ordinal numbers may be placed before or after the nound.

el primer día  = the first day 
el día primer  = the first day

Note: if you use a cardinal number in place of an ordinal number it usually follows the noun:
el día diecisiete = the seventeenth day

In address where a floor number is given it is generally expressed as the number followed by a "o".

4o = the fourth floor

For royalty and popes ordinal numbers are used only through décimo (10th).  The definite article "the" (el) is omitted and "nono" replaces "noveno".

Carlos Quinto = Charles V or Charles the Fifth
Alfonso Trece  = Alfonso XIII or Alfonso the Thirteenth
Pío Nono    = (Pope) Pius IX or (Pope) Pius the Nineth


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