annähernd
approximately
Not exact, but very close to a certain value, amount, or quality; roughly, almost.
Die Reparatur wird annähernd 500 Euro kosten.
The repair will cost approximately 500 euros.

approximate / approximately
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approximately
Not exact, but very close to a certain value, amount, or quality; roughly, almost.
Die Reparatur wird annähernd 500 Euro kosten.
The repair will cost approximately 500 euros.

The word derives from the verb 'sich annähern' (to approach). When something 'annähernd' (approximately) corresponds to a value, it 'nähert sich' (approaches) that value without reaching it exactly.
Die Zahl der Teilnehmenden war annähernd so hoch wie im letzten Jahr.
The number of participants was approximately as high as last year.
'Annähernd' (approximately) is mostly used as an adverb and comes directly before the number, amount, or adjective it describes. In this function, it is not declined.
Wir haben annähernd 100 Bewerbungen erhalten.
We received approximately 100 applications.
'Annähernd' (approximately) belongs more to written language or a more formal style. It is often used in reports, news, or scientific contexts.
Die gemessenen Werte waren annähernd identisch.
The measured values were approximately identical.
exact / precise
'genau' and 'annähernd' are opposites when it comes to values, quantities, or descriptions. 'genau' means that something is exactly right and has no important deviation. 'annähernd' means that something is only almost right or comes very close to a value. If a number is truly precise, 'genau' fits. If you are only giving an approximate but close figure, 'annähernd' is more natural.

Nach dem Umbau war der Garten annähernd so groß wie vorher.
After the renovation, the garden was almost as large as before.
Die Verkäuferin sagt genau, wann der Zug für die Reise abfährt.
The saleswoman says exactly when the train for the trip departs.