nahezu
almost
Almost, nearly, or approximately. It expresses that a state or quantity has almost been reached.
Nach der langen Wanderung war die Wasserflasche nahezu leer.
After the long hike, the water bottle was almost empty.

almost
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almost
Almost, nearly, or approximately. It expresses that a state or quantity has almost been reached.
Nach der langen Wanderung war die Wasserflasche nahezu leer.
After the long hike, the water bottle was almost empty.

The word is made up of 'nahe' (near) and 'zu' (to). Literally, it expresses that you 'come close' to something or a state, but do not quite reach it.
Wir sind dem Ziel schon sehr nahe.
We are already very close to the goal.
'Nahezu' (almost) belongs more to written language or to an elevated, more formal style. It is used less often in everyday spoken language.
Die Aufgabe war nahezu unmöglich zu lösen.
The task was almost impossible to solve.
'Nahezu' (almost) often comes before adjectives or participles to describe an approximation to a state. Common combinations are 'nahezu unmöglich' (almost impossible), 'nahezu identisch' (almost identical), 'nahezu abgeschlossen' (almost completed), or 'nahezu perfekt' (almost perfect).
Die beiden Bilder sind nahezu identisch.
The two pictures are almost identical.
about / approximately
'etwa' and 'nahezu' can both make a statement less exact. The important difference is: 'etwa' means 'about' or 'approximately' and gives a number or amount only roughly. 'nahezu' means 'almost' and shows that something has nearly been reached. Learners may confuse the words because both make statements that are not completely exact. As a practical rule: for an approximate number, 'etwa' usually fits. When something is almost complete or almost reached, 'nahezu' fits better.

Nach dem langen Regen war der Keller nahezu voll mit Wasser.
After the long rain, the basement was almost full of water.
Die Fahrt zum Bahnhof dauert etwa zwanzig Minuten.
The trip to the train station takes about twenty minutes.