Dramatic SpaceX video shows what happens when a rocket's nose cone pops off

Good catch! They obviously want to pop the fairing when atmosphere drag is no longer a problem.

I googled that SpaceX use a fairly constant 150ish km altitude, which is above the Karman line at 100 km, which is when you can in theory propel a low Earth orbit satellite in orbit. It is rather the altitude of many low Earth orbit satellite which are later either propelled up or spontaneously dragged down over many orbits.

The scale height (the atmosphere height where you have passed 1-1/e or 60 % of atmosphere mass) of Earth is a low 8 km, which is easy to remember - Mount Everest climbers breathe 60 % of ocean height oxygen - and nothing like the scale height of 1.5 Earth atmosphere pressure Titan which scale height is something like ~ 100 km - but then again colder atmospheres are non-intuitively higher.

If the atmosphere density goes exponential as the scale height measure suggest, another 10 e-folds would give you something like e^-10 or ~ 2^-10 or ~ 10^-5 atmospheres density.