file / act
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file
A collection of documents and written materials about a specific case, person, or topic, usually kept in a folder.
Der Anwalt hat die Akte des neuen Mandanten sorgfältig studiert.
The lawyer carefully studied the new client's file.
In connection with documents, 'Akte' (file) is often combined with certain verbs. You can say 'eine Akte anlegen' (to create a file), 'eine Akte schließen' (to close a file), or 'Einsicht in eine Akte nehmen' (to inspect/read a file).
Die Polizei hat für den Fall eine neue Akte angelegt.
The police opened a new file for the case.
The word 'Akte' (file) is often part of compound nouns that describe the contents more precisely. Common examples are 'Personalakte' (personnel file, about an employee), 'Krankenakte' (medical file, about a patient), or 'Polizeiakte' (police file, about a criminal case).
Alle wichtigen Informationen über den Patienten stehen in seiner Krankenakte.
All important information about the patient is in his medical file.
The idiom 'etwas zu den Akten legen' (to file something away) is a fixed unit. The 'etwas' is replaced by the matter you consider settled. The form 'zu den Akten' remains unchanged.
Wir haben uns geeinigt, also können wir den Streit zu den Akten legen.
We have reached an agreement, so we can file the argument away.
documents / mat
'Unterlagen' and 'Akte' both have to do with collected papers. 'Unterlagen' is more general and means documents you need for a purpose, for example for an application or an appointment. An 'Akte' is more like an organized collection about a specific case, person, or topic, often in an office, at an authority, or with the police. The words can be confused because an 'Akte' can consist of many 'Unterlagen'. If you just mean the necessary papers, 'Unterlagen' is a better fit; if you mean the whole organized case file, 'Akte' is a better fit.
Im Büro sucht sie die Akte des Kunden im Schrank.
In the office, she looks for the customer's file in the cabinet.
Vor dem Gespräch legt Mehmet seine Unterlagen auf den Tisch.
Before the meeting, Mehmet puts his documents on the table.