
ungefähr
approximately
Not exact, but only estimated or approximate.
Die Reparatur wird ungefähr 200 Euro kosten.
The repair will cost approximately 200 euros.
approximately
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approximately
Not exact, but only estimated or approximate.
Die Reparatur wird ungefähr 200 Euro kosten.
The repair will cost approximately 200 euros.

by chance
By chance, unexpectedly, or for no apparent reason.
Sein Erfolg kam nicht von ungefähr, er hat jahrelang dafür gearbeitet.
His success didn't come by chance; he worked for years to achieve it.
The adverb 'ungefähr' (approximately) normally stands directly before the number, quantity, or time expression that it makes inexact.
Ich bin in ungefähr zehn Minuten bei dir.
I'll be with you in approximately ten minutes.
The expression 'von ungefähr' (by chance) is almost always negated: 'nicht von ungefähr kommen' (not to come by chance). This means that something has a good reason and is not a coincidence.
Ihre Beförderung kommt nicht von ungefähr; sie hat sehr hart gearbeitet.
Her promotion didn't come by chance; she worked very hard.
The word is made up of 'un-' and 'Gefahr' (danger). Although today it means 'geschätzt' (estimated), the original idea was 'without danger.' This origin helps explain why it refers to an estimate that is considered safe or plausible.
Ich weiß nicht genau, wie viele Leute kommen, aber es werden ungefähr fünfzig sein.
I don't know exactly how many people are coming, but it will be approximately fifty.
about / approximately
For an estimated number, etwa and ungefähr both indicate that the figure is not exact. Etwa often sounds a little more concise and can also have other functions depending on the sentence; ungefähr clearly indicates an approximation. For a simple estimate, either word works well.

Die Strecke ist ungefähr zehn Kilometer lang.
The route is approximately ten kilometers long.
Die Strecke ist etwa zehn Kilometer lang.
The route is about ten kilometers long.