performance / appearance
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performance
The performance of an artist or group on a stage in front of an audience, for example in the theater, at a concert, or in the circus.
Der Auftritt der Band am Samstag war komplett ausverkauft.
The band's performance on Saturday was completely sold out.
The noun 'der Auftritt' comes from the separable verb 'auftreten' (to appear/perform). The verb literally means 'to step onto a stage' and describes the action, while the noun is the result or the event itself.
Die Sängerin tritt heute Abend zum ersten Mal in Berlin auf.
The singer is performing in Berlin for the first time tonight.
When referring to an artistic performance, 'Auftritt' (performance) is often combined with the verb 'haben' (to have). For example, you can have a performance at a festival or on television.
Die junge Band hatte gestern ihren ersten großen Auftritt.
The young band had their first big performance yesterday.
To describe a person's public behavior, 'Auftritt' (appearance/manner) is often combined with adjectives that evaluate their presence. Typical examples are 'ein selbstsicherer Auftritt' (a confident appearance), 'ein professioneller Auftritt' (a professional appearance), or 'ein souveräner Auftritt' (a poised/confident appearance).
Mit ihrem kompetenten Auftritt konnte sie die Investoren überzeugen.
With her competent appearance, she was able to convince the investors.
The expression 'jemandem einen Auftritt machen' means to cause a loud, dramatic, and often unpleasant scene. It is usually used when someone is reproaching another person.
Als er die Rechnung sah, machte er dem Kellner einen lauten Auftritt.
When he saw the bill, he made a loud scene with the waiter.
number
'die Nummer' and 'der Auftritt' can both be part of a show or event. 'die Nummer' means an individual item in the program, for example a song, a trick, or a short dance. 'der Auftritt' refers more to the whole performance of a person or group in front of an audience. So a performance can consist of one or more acts. The words can be confusing because both happen on stage. If you mean the item in the program, 'Nummer' fits better; if you mean that someone appears and performs in front of an audience, 'Auftritt' fits better.
Beim Schulfest hatte die Band ihren ersten Auftritt.
At the school festival, the band had their first performance.
Die letzte Nummer im Zirkus war besonders lustig.
The last act in the circus was especially funny.