careful / cautious
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careful
Acting with care and attention in order to avoid dangers, mistakes, or damage.
Sei bitte vorsichtig, der Boden ist frisch gewischt und sehr rutschig.
Please be careful, the floor has just been mopped and is very slippery.
The word is made up of 'Vor-' and '-sichtig' (from Sicht/sehen, sight/to see). Literally, it means 'foresighted,' that is, looking ahead in order to avoid dangers.
Ein vorsichtiger Kletterer prüft jeden Griff zweimal.
A careful climber checks every handhold twice.
Like many adjectives, 'vorsichtig' (careful/carefully) can also be used as an adverb to describe how an action is carried out. It then remains unchanged after the verb.
Fahr bitte vorsichtig, die Straßen sind glatt.
Please drive carefully, the roads are icy.
To mark a restrained statement, 'vorsichtig' (cautious/cautiously) is often combined with words like 'Schätzung' (estimate), 'Prognose' (forecast), or 'Optimismus' (optimism).
Ich bin vorsichtig optimistisch, dass wir das Projekt rechtzeitig abschließen.
I am cautiously optimistic that we will finish the project on time.
quiet
'leise' and 'vorsichtig' can both describe a way of doing something. 'leise' emphasizes that something happens almost inaudibly or gently. 'vorsichtig' emphasizes that someone acts attentively so that nothing breaks or no mistake happens. The words can fit the same situation, but they do not mean the same thing. Someone who closes a door 'leise' makes little noise. Someone who closes a door 'vorsichtig' makes sure not to slam or damage it.
Sofia trägt die heiße Suppe vorsichtig zum Tisch.
Sofia carefully carries the hot soup to the table.
Nach dem Essen räume ich leise die Küche auf, weil meine Freundin telefoniert.
After dinner, I quietly tidy up the kitchen because my girlfriend is on the phone.