pennen
to sleep
Colloquial expression for sleeping.
Ich bin total müde, ich geh jetzt pennen.
I'm totally tired; I'm going to sleep now.

to sleep / to space out
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to sleep
Colloquial expression for sleeping.
Ich bin total müde, ich geh jetzt pennen.
I'm totally tired; I'm going to sleep now.

'Pennen' (to sleep / to space out) is a very informal, colloquial word. Use it only with friends or in casual situations, but not in formal emails or at work.
Sorry, ich kann heute Abend nicht, ich will nur noch pennen.
Sorry, I can't tonight; I just want to sleep.
In the meaning 'schlafen' (to sleep), 'pennen' is often used with 'bei jemandem pennen' (to sleep over at someone's place) or 'tief und fest pennen' (to sleep very soundly).
Nach der Party kann ich bei einem Freund pennen.
After the party, I can sleep over at a friend's place.
In the meaning 'unaufmerksam sein' (to be inattentive), the fixed expression '(da) habe ich gepennt' (I spaced out there) is almost always used in the perfect tense. It expresses that you made a mistake or missed something important.
Ich habe die Ankündigung nicht gehört, da habe ich wohl gepennt.
I didn't hear the announcement; I must have spaced out.
to sleep
'schlafen' and 'pennen' can both mean that someone is sleeping. The most important difference is style: 'schlafen' is neutral and works almost everywhere, including in polite or factual situations. 'pennen' is colloquial and sounds casual, sometimes also a bit rough. It is normal among friends, but less so in a conversation with a doctor or in formal texts. Both words can also mean that someone was inattentive. Here too, 'pennen' is clearly colloquial, for example in 'Da habe ich gepennt' (I spaced out there).

Pennst du am Wochenende wieder bei Max?
Are you sleeping over at Max's again this weekend?
Er schläft heute früh, weil er morgen arbeiten muss.
He is going to sleep early today because he has to work tomorrow.