careful
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careful / carefully
Done with great attention, accuracy, and conscientiousness. It describes an action or the quality of a person who works very precisely and thoroughly.
Sie prüfte das Dokument sorgfältig auf Fehler.
She carefully checked the document for errors.
'Sorgfältig' (careful/carefully) is the adjective related to the noun 'die Sorgfalt' (care/diligence). Both words describe accuracy and attention in an activity.
Bitte erledigen Sie diese Aufgabe mit der nötigen Sorgfalt.
Please complete this task with the necessary care.
'Sorgfältig' (carefully) is very often used as an adverb to describe HOW an action is carried out. It then usually appears directly with the verb.
Der Arzt untersuchte den Patienten sorgfältig.
The doctor examined the patient carefully.
The word often describes actions that require accuracy. Typical verbs are: 'sorgfältig prüfen' (to check carefully), 'sorgfältig auswählen' (to select carefully), 'sorgfältig planen' (to plan carefully), and 'sorgfältig arbeiten' (to work carefully).
Wir müssen die Kandidaten für die Stelle sorgfältig auswählen.
We have to select the candidates for the position carefully.
exact / precise
'genau' and 'sorgfältig' both have to do with good work with few errors. 'genau' emphasizes the result or the precision: a piece of information, drawing, or check is exactly right. 'sorgfältig' emphasizes more the way someone works: calmly, attentively, and thoroughly. They can be confused because careful work often leads to precise results. If you are describing the result, 'genau' fits better. If you are describing the way of working, 'sorgfältig' is more natural.
Vor der Prüfung liest Lena ihre Notizen sorgfältig durch.
Before the exam, Lena carefully reads through her notes.
Simon hat bei der Arbeit genau gemessen.
Simon measured precisely at work.