der/die/das vierte
fourth
The ordinal number for the number 4, indicating a position in a sequence.
Sie wohnt im vierten Stock.
She lives on the fourth floor.

fourth
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fourth
The ordinal number for the number 4, indicating a position in a sequence.
Sie wohnt im vierten Stock.
She lives on the fourth floor.

The word 'viert' (fourth) belongs to the word family of 'vier' (four). It is the ordinal number, while 'vier' is the cardinal number and 'das Viertel' (the quarter) refers to the fraction (¼).
Vier Läufer starten, aber nur der vierte kommt aus Deutschland.
Four runners start, but only the fourth comes from Germany.
As an ordinal number, 'vierte' (fourth) is used like an adjective before a noun and must be declined. The ending changes depending on the article and case.
Wir feiern heute den vierten Advent.
Today we are celebrating the fourth Sunday of Advent.
The construction 'zu viert' (as a group of four / the four of us) is a fixed expression used to describe the size of a group. It answers the question 'Wie viele Personen?' (How many people?). The structure is 'zu' + number + 't'.
Wir waren zu viert im Kino.
The four of us were at the movies.
four
'vier' and 'viert' are both connected to the number 4, but they are used differently. 'vier' names the quantity: there are four people or four things. 'viert' belongs to order or sequence, for example 'der vierte Tag' (the fourth day). In the form 'zu viert', it means that four people are together. Learners may confuse the words because they look similar. As a simple guide: quantity is 'vier', order is 'vierte', and a group of four people is 'zu viert'.

Am Samstag gehen wir zu viert ins Kino.
On Saturday, the four of us are going to the movies.
Für den Kuchen brauche ich vier Eier.
I need four eggs for the cake.