ununterbrochen
uninterrupted
Without a pause or interruption; continuous and ongoing.
Er hat zehn Stunden ununterbrochen gearbeitet, um das Projekt fertigzustellen.
He worked uninterrupted for ten hours to finish the project.

uninterrupted
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uninterrupted
Without a pause or interruption; continuous and ongoing.
Er hat zehn Stunden ununterbrochen gearbeitet, um das Projekt fertigzustellen.
He worked uninterrupted for ten hours to finish the project.

The word is made up of the prefix 'un-' and 'unterbrochen' (interrupted), the past participle of 'unterbrechen' (to interrupt). The prefix 'un-' negates the word, so 'ununterbrochen' literally means 'not interrupted'.
Der Lärm von der Baustelle war ununterbrochen zu hören.
The noise from the construction site could be heard uninterrupted.
'Ununterbrochen' can stand before a noun as an adjective or function as an adverb describing a verb. As an adjective it is declined; as an adverb it remains unchanged.
Nach drei Stunden ununterbrochener Fahrt machten wir eine Pause.
After three hours of uninterrupted driving, we took a break.
The word is often used to describe continuous actions or states. Typical combinations are 'ununterbrochen reden' (to talk uninterruptedly), 'ununterbrochen arbeiten' (to work uninterruptedly), as well as 'ununterbrochener Regen' (uninterrupted rain) and 'ununterbrochener Applaus' (uninterrupted applause).
Sie redete zwei Stunden lang ununterbrochen über ihre Reise.
She talked uninterrupted for two hours about her trip.
round / about
'rund um die Uhr' and 'ununterbrochen' can both express that something happens without a pause. 'rund um die Uhr' specifically means 24 hours a day, that is, day and night. It is often used for services, help, or work. 'ununterbrochen' is more general: it only says that something continues without a pause, even if it only lasts a few hours. If you mean exactly 24 hours, 'rund um die Uhr' fits better. If only the lack of a pause is important, 'ununterbrochen' is more precise.

Seit dem Morgen hat es ununterbrochen geregnet.
It has been raining continuously since this morning.
Die Hotline ist rund um die Uhr erreichbar.
The hotline is available around the clock.