Estimate for a standard classroom globe at 13" in diameter (I'm seeing a rnage of 12-14 inches as typical). I'm reporting in inches because that is what came up first and most of the globes are for sale in the US. Mixing units here, but, it works out.
But, in meters, the diameter of the Earth is 12,742,000 m on average. if we use the 'Karman line' as defining the edge of what the atmosphere is, that is 100,000 meters. Solving for X ... (13" / 12742000 m)=(X / 100,000 m). gives us an atmosphere thickness of approximately 0.1". -----
Paper glued to the globe would have a thickness of maybe, 0.004" (thin paper) to 0.012" (like a card stock paper).... so that analogy is off by an order of magnitude or more.
Even if you use the mesosphere as the definition for the top of the atmosphere, that is still 85,000 meters and thus similar.
People can check the numbers I used.
* Perhaps the analogy should go more like: the thickness of the cardboard sphere the globe is made out of is about the thickness of the atmosphere. Because, having completely destroyed a globe once in my youth, I remember the cardboard shell being approximately a tenth of an inch thick. But, that's maybe not a great reference for the analogy because not everyone has cut apart a classroom globe....
90% of the atmosphere is below 16 km.
16 km * (12" / Earth diameter) :: https://www.wolframalpha.com/input?i=16+km+*+%2812%22+%2F+Ea...
0.015 inches, 0.38 mm
... and tossing sheets of paper into that ( https://www.wolframalpha.com/input?i=thickness+of+paper ) ...
16 km * (12" / Earth diameter) / thickness of paper :: https://www.wolframalpha.com/input?i=16+km+*+%2812%22+%2F+Ea...
4
Note that that's copy paper rather than card stock...
Adjusting this to 5.6km (the 50% atmosphere amount) ...
5.6 km * (12" / Earth diameter) / thickness of paper :: https://www.wolframalpha.com/input?i=5.6+km+*+%2812%22+%2F+E...
1
So it's a matter of selecting the proper globe, proper paper, and proper threshold for the atmosphere.
I think this thread would also be loved by the nerdy folks at https://Reddit.com/r/theydidthemath
... and the source document for the numbers was based on a paper that is fairly easy to find given the proper keywords in google search... https://pubmed.ncbi.nlm.nih.gov/1648028/ (and I learned that methane more rare in flatus than not).
Another comment talks about atmosphere being a 1 mm layer on a grapefruit... so definition of atmosphere extents might be different in these two anecdotes.
(edit: I submitted this comment two minutes after another comment did the math on the globe/paper layer version...)