Here are the ordinal numbers first - tenth:

primero
first sexto
sixth
segundo
second séptimo
seventh
tercero
third
octavo
eighth
cuarto
fourth
noveno
ninth
quinto
fifth décimo
tenth

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Like many other adjectives, the ordinal numbers have a masculine and a feminine form.

primero
primera
sexto
sexta

segundo
segunda
séptimo
séptima

tercero
tercera
octavo
octava

cuarto
cuarta
noveno
novena

quinto
quinta
décimo
décima

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They also have a singular and plural form.

primero
primeros
sexto
sextos

segundo
segundos
séptimo
séptimos

tercero
terceros
octavo
octavos

cuarto
cuartos
noveno
novenos

quinto
quintos
décimo
décimos

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So, the ordinal numbers have four forms, just like other adjectives that end in -o.

primero
primeros
primera
primeras

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Primero and tercero drop the -o in the masculine singular adjective form.

el primer día
el tercer año

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Ordinal numbers usually precede the noun. However, if the noun they refer to is royalty, a pope, or a street, they come after the noun.

Carlos Quinto
("Quinto" comes after "Carlos" - royalty)

el quinto libro
("quinto" comes before "libro")

la Calle Sexta
("sexta" comes after "calle" - street)

la sexta pluma
("sexta" comes before "pluma")

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Ordinal numbers are not normally used after 10.

la Calle Dieciséis
Sixteenth Avenue

el siglo diecinueve
the nineteenth century