haven't got time for this

Duhhhhhh.

But why did they choose that value - and not 10 billion periods even? To approximate an astronomical measure of 1 / 86400 of a day?

Of course it is a geometric measurement. and humans have a fascination with circles. I guess it may have begun with stars in the night sky when people first began noting their movement. Primitive man would have noted that seasons come around regularly, and as they did the same constellations would appear in certain parts of the sky. To them, if they were keeping any sort of count, roughly 360 days in a year so the sky would have been divided into 360 segments which we now call degrees. In geometry we divide each degree into 60 minutes, which are then divided into 60 seconds. We did the same with clocks, the time span of seconds only came about with grandfather clocks. The world moved to decimal and metric systems because we have 10 fingers, the old imperial measurements were based on natural units as far as I can tell. Hands, feet, yards and so on. Humans are rarely able to make a rapid transition, hence all major cities built on rivers for transportation, then requiring bridges as roads became the norm. I love the reason space shuttle engines are not as wide as the engineers developing them would have liked.

Reminds me of having spaced out watching the digital reader board at the US Naval Observatory in Washington, D.C. It “maintains 57 HP/Agilent/Symmetricom 5071A-001 high performance cesium atomic clocks and 24 hydrogen masers.” ...I believe the Vice President’s home is ‘next door’