
genau
exactly
As an adverb: exactly, precisely, right on the mark.
Das ist genau das, was ich gemeint habe.
That is exactly what I meant.
exact / precise
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exactly
As an adverb: exactly, precisely, right on the mark.
Das ist genau das, was ich gemeint habe.
That is exactly what I meant.

exact / precise
As an adjective: exact, precise, careful, and without errors.
Für diese Arbeit brauchen wir eine genaue Messung.
For this work, we need a precise measurement.

exactly
As a particle or interjection: expresses agreement or confirmation; means 'richtig' (right) or 'stimmt' (that's correct).
Wir treffen uns also morgen um zehn? - Genau!
So we're meeting tomorrow at ten? - Exactly!
'Genau' can be used as an adjective before a noun or as an unchanging adverb. As an adjective, it is declined; as an adverb, it always stays the same.
Das ist eine genaue Kopie des Originals.
That is an exact copy of the original.
In conversation, 'Genau!' is very commonly used as a short, confirming answer. It means 'Richtig!' (Right!) or 'Das stimmt exakt!' (That's exactly correct!) and can stand on its own.
Du meinst also, wir sollten den anderen Weg nehmen? – Genau!
So you mean we should take the other way? – Exactly!
As an adverb for emphasis, 'genau' often stands directly before the word it specifies. Common combinations are 'genau das' (exactly that), 'genau hier' (right here), 'genau so' (exactly like that), or 'genau richtig' (exactly right).
Das ist genau der Pullover, den ich kaufen wollte.
That is exactly the sweater I wanted to buy.
As an adjective, 'genau' often describes things that require precision. Typical combinations are 'eine genaue Beschreibung' (a precise description), 'genaue Anweisungen' (precise instructions), or 'eine genaue Uhrzeit' (an exact time).
Für die Montage brauchen wir eine genaue Anleitung.
For the assembly, we need precise instructions.
correct / right
Genau and richtig can express agreement in a short reply. Richtig mainly evaluates a statement as accurate or free of errors, while genau more strongly confirms that it precisely addresses the point meant. Richtig fits a factual correction, while genau is often used when there is exact agreement.

Genau, der Termin beginnt um neun Uhr.
Exactly, the appointment starts at nine.
Richtig, der Termin beginnt um neun Uhr.
Correct, the appointment starts at nine.