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An Apple for a Dollar 
Title text: I'd like 0.4608 apples, please. 
Explanation
Megan is about to buy an apple at a grocery store when she is surprised that the price is exactly one dollar. In most cases in the US, sales tax must be taken into account, and it is not included in the list price, but most states exempt food sold in grocery stores, so the price comes out to a round value. This is so strange for Megan that it throws her for a loop. Buying one apple for one dollar feels to her more like a simplified, imaginary Idea of a transaction (a "Platonic Ideal") than like something that could actually happen in real life.
Megan likely shares Randall's background of engineering and math. When learning science, engineering, and math in the education system, one studies examples where every number is some round value, and all situations are simplified to the barest essentials so as to demonstrate the ideas being taught. Then, when doing real problems in the real world, one spends the rest of one's life almost never being able to use the simplified tricks demonstrated as examples in school, because when math is used to describe the natural world, nothing is ever a round number unless by design.
Megan references Platonic Idealism, which is the theory attributed to Plato that abstract or nonphysical Ideas represent the purest, most accurate version of reality, but we can only perceive of more flawed versions of Ideas because of our limited viewpoint (as explained in his Allegory of the Cave). Thus we can understand the concept of a perfect circle or a perfect line, even though we have never seen one, and cannot create one. Megan believes she has glimpsed a Platonic Ideal, because the absolute concept of currency is it is the exact worth of something in trade. Megan is awed because if this is true, than she is witnessing the next layer of reality, which Plato often compared to heaven.
The harsh difference between being able to buy an apple for a dollar at this quaint store, and having to deal with arbitrary decimals and numbers in the rest of life could be touching on Megan's life experience of the world not being what she was prepared for, resulting in her intense response. Regardless if that is true or not, it seems the cashier is unable to figure out how to handle it (or does not want to), and raises the price to an arbitrary nonrounded value, which has the intended effect of halting Megan's outburst.
Megan's references refer to common parameters used in solving science or math questions. A Frictionless plane is a scenario from the writings of Galileo to calculate the movement of an object down an inclined plane, since his equations did not account for friction.
"A train leaving Chicago at 40 mph" refers to common math questions, involving trains and solving for the distance required to overtake said train, although this problem involves the rather unrealistic assumption that the train's velocity keeps constant. Like the frictionless plane, this is a common simplification that allows the problem to be solved with quite simple techniques, just like having round quantities (e.g. 1 dollar/apple) eases arithmetic problems. See also 669: Experiment. Apples themselves are commonly used as units for math problems, including problems as simple as basic arithmetic.
The comic repeats a common theme in the strip of engineers and computer scientists trying to apply their technical experience to social situations. In this case, the conversation partner is "normal", and does not respond supportively, which is a common situation in the real world and a possible point of empathy with readers.
It seems that according to the title text, Megan only has (or only wants to spend) one dollar, so she would not be able to buy a whole apple at the new price (0.4608 × $2.17 ≈ $1). Stores usually sell whole apples, so asking for a fraction of one is not likely to work out.^{[citation needed]}
Transcript
 [Megan is at the store counter, behind which Ponytail (the cashier) is waiting.]
 Megan: Just this apple, thanks.
 Ponytail: That will be one dollar.
 Megan: Exactly? No tax or anything?
 Ponytail: That's right.
 [Megan stares at the apple in a frameless panel.]
 [Scene zooms in on Megan.]
 Ponytail: ...Is that a problem?
 Megan: It's just weird to realize that every other transaction in my life will be more complicated than this.
 [Scene changes focus to Ponytail behind the counter.]
 Megan: This is like a platonic ideal exchange. An apple for a dollar.
 Ponytail: I see.
 [Scene changes back to Megan, once again lost in profound contemplation of the apple.]
 Megan: Are we on a frictionless plane? Is a train leaving Chicago at 40 mph? Should I solve for something??
 Ponytail: Okay, apples are $2.17 now.
 Megan: That's... probably better for us both.
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