Yes, I know this is a pretty random number.
Why not 0.09 BTC or 0.12 BTC?
I think having one tenth of a full bitcoin is a great psychological milestone. That's 10 million sats.
In a hyperbitcoinization scenario, 0.10 BTC is going to be a huge amount of money. And even if we don't go hyper, I'm sure 0.10 BTC is going to work great as an emergency fund in the near future.
You won't be able to afford buying 0.10 BTC in a few years. Do it now that it's only $3k or less.
Other milestones I like:
0.33 BTC (one third of a bitcoin)
0.50 BTC (half a bitcoin)
1 BTC (whole coiner)
3 BTC (probably enough to retire in the next 5 years or so)
10 BTC (multimillionaire status)