As Halloween approaches, Nurcan gains a reputation for Arithmancy prowess, and, to a lesser extent, History of Magic. At the same time, her French has improved significantly. For the first time, she contemplates charging people asking for aid in these courses.

  "Peux-tu m'aider en arithmancie?" (Can you help me in Arithmancy?) Nacien, a third-year student, asks her, crying while brandishing a problem set from first-year arithmancy.

  "C'est pas gratuit..." (It's not free!) Nurcan exclaims.

  "Combien c'est?" (How much?)

  "Admettons un bézant pour le devoir..." (Let's say a bezant for the assignment)

  Oh my God... at this rate, I think I can get my owl before Yule Ball, let alone Ramadan! But I don't think they will let me do Ramadan unless I could somehow frame it as a magical ritual! Nurcan starts thinking about the financial implications of tutoring the kids in Arithmancy. But as the price is readily agreed upon, and perhaps a little expensive for what she knows, she gets the boy to the library and set out to work their way through a problem set.

  Apparently, said problem set is about the use of arithmancy in potion-making. More specifically, operations on significant digits as well as uncertainties in taking potion-making measurements.

  "Le problème a plusieurs étapes. Quand faut-il arrondir?" (The problem has multiple steps. When to round the number?) the third-year student asks her, unsure of how to go around doing the calculation.

  "à la fin!" (At the end!)

  Nurcan then proceeds to explain to him how rounding intermediate results can introduce parasitic errors by doing the calculations once with intermediate rounding and once more without it.

  At this point, a Lumos charm seems to be cast in Nacien's mind, and he understands a little better how rounding works when dealing with a chain of calculations.

  However, another concept that seems to trip people up, related to operations with significant figures, is operations with uncertainties.

  "Pourquoi devrais-je additionner les incertitudes si je soustrais deux nombres?" (Why should I add the uncertainties if I'm subtracting two numbers?) that student adds, before Nurcan illustrates what range of values the composite value could take.

  Such as what would happen if one prepared a vial containing streeler shells whose total mass is (30.0 + 0.1)g to brew a hair-dyeing potion, but now one realizes that they need to consider the vial's tare, or empty, mass of (20.0 + 0.1)g to ensure they have the correct quantity of streeler shells.

  There would now be (10.0 + 0.2)g of it in the cauldron, because the full vial might be as little as 29.9g, or as much as 30.1g, at the onset, and its tare might be as little as 19.9g or as much as 20.1g, so, in the end, there might be between 9.8g and 10.2g of streeler shells.

  "Là je comprends!" (Now, I understand!)

  That assignment looks way too much like a midterm exam. Makes me wonder how they could go around taking 2 years of Potions without knowing about uncertainty and the consequences of uncertain measurements when brewing potions! To think this place is supposed to be good at alchemy, and all I can make out is that alchemy builds upon potion-making! Nurcan's face turns red as she struggles to contain her frustrations about how people at Beauxbatons could accept such faulty methods.

  "Il y a quelque chose qui cloche avec toi!" (There's something wrong with you!) the tutee points out when they get to the total uncertainty, and hence significant digits, in multiplication.

  "C'est personnel!" (It's personal!)

  The main complication, when multiplying numbers with uncertainties, is that their relative uncertainties must be calculated first, then added and finally, the total relative uncertainty, expressed in decimal form, must be multiplied by the product (or quotient).

  But it gets trickier for the third-year student to understand exactly how uncertainties carry over when multiplying or dividing numbers. So long as one isn't doing so with an integer number, in which case it has no relative uncertainty.

  "Voilà, ton bézant!" (There, your bezant!) the third-year tutee hands her a coin for Bz1.

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  This late at night, after she helped one student get through key arithmancy concepts used in potion-making, for Bz1, she starts crying, but this time it's not about what she perceives as teaching about significant figures and uncertainties too late for their own good.

  (Loosely translated from Turkic) "What am I doing here? I feel like I'm letting the Empire down! I might be tutoring peeps in Arithmancy but what do I have to show for it? Nothing I couldn't have gotten at home! The Sultan will be really angry if I return home empty-handed, at year-end! Right now, it feels like it's France that benefits, and unilaterally!" Nurcan cries a river, which doesn't go unnoticed by the three roommates present in the room.

  "Je n'y comprends rien!" (I don't understand!) Emmanuelle clamors over this rant in Turkic. "Tu sembles t'en tirer!" (You appear to do just fine!)

  "C'est pas que je réussis pas..." (It's not that I'm not doing well...)

  Let's see: I'm just as dominant in Arithmancy here as I was at home, and I'm not worried about Potions, History of Magic either. Yet, I have the same weakness in Transfiguration as I have at home... but I might be bottlenecked in it by being underpowered, Nurcan reflects on how she seems to be doing up to this point.

  "C'est vrai, tu es forte comme une Turque en classe!" (It's true, you're as strong as a Turk in class!) Alejandra comments on her academic prowess.

  "C'est quoi le problème, alors?" (What's the problem, then?) Isabella asks her.

  Nurcan faces both Alexandra and Isabella, with her face still showing some tears. "Vous n'avez pas oublié que je suis Turque?" (You didn't forget that I'm Turkish?) she asks the two of them. "On dirait que vous recevez tout! J'aurais souhaité que cet échange en soit réellement un..." (It seems you receive everything! I wished this exchange to actually be one...)

  Isabella struggles to understand her roommate's feelings, and asks more questions. "Qu'est-ce qui, selon toi, compte dans un échange étudiant?" (What does she think counts in a student exchange?)

  This statement gives Nurcan pause, while the other two seem puzzled and amused. At the same time, it makes them think, too.

  Why does she feel like the exchange is one-sided? I understand the need to feel like an exchange should be a give-and-take kind of thing, sure... Emmanuelle ruminates as she's left wondering what counts and what doesn't.

  "As-tu l'impression de ne rien apprendre?" (Do you have the impression of not learning anything?) Alejandra asks a clearly distressed Nurcan.

  "C'est pas que je n'apprends rien, c'est que ce que j'apprends ici ne fait pas de moi une meilleure personne, pas plus que ?a soit d'intérêt impérial!" (It's not that I don't learn anything, it's that what I learn here doesn't make me a better person any more than it is of Imperial interest!) Nurcan keeps crying, while the others, clearly clueless about Ottoman goings-on, roll their eyes. "Vous, cependant, faites face à un gros problème d'arithmancie!" (You, on the other hand, face a big arithmancy problem!)

  "De quoi tu parles?" (What are you talking about?) Emmanuelle rolls her eyes.

  The others can definitely feel Nurcan's distress coming, but they all tune her out when Arithmancy is mentioned, because none of them are taking it. And, on exchange, host schools try to ensure the students they host aren't falling behind upon return at their home institutions. There's no reason for me to take Arithmancy here otherwise.

  But when the Potions class rolls around, at the end of the following day, after the Potions midterm ends, Nurcan voices her complaint her roommates ignored the previous night to the Potions prof.

  "Je demande des explications sur pourquoi on ne couvre pas les chiffres significatifs et les calculs d'incertitudes en potions!" (I ask for explanations for why significant figures and uncertainty calculations aren't covered in Potions!)

  "Tu comprends que tu es loin d'être une étudiante ordinaire?" (You do understand you're far from an ordinary student?) the potions prof asks her, taken aback.

  "Pourquoi?" (Why?)

  "Ce dont tu te plains serait assez difficile pour un étudiant de première, ou même de deuxième année. Tu y arrives sans peine, mais..." (What you're complaining about would be rather difficult for a first-year, or even a second-year student. You do it without trouble, but...)

  "Je reconnais que c'est pas tout le monde qui peut être aussi bon que moi..." (I acknowledge not everyone can be as good as I am...) Nurcan sighs.

  I know this because I tutored someone on these topics last night! She muses while they discuss the implications of uncertainty calculations for potion-making, which are, admittedly, ingredient-dependent.

  And, of course, how focused on ingredient properties the early stages of potion-making learning, and how does that translate to the resulting potions.

  So first and second-year potions are less sensitive to "excess ingredient effects"? Nurcan comes to a grim realization as to why potion-making curriculum let students brew potions without having to deal with significant figures and uncertainty calculations. Why is it that it took years for me to realize that? They might have had good reason not to expose them to these topics, but it was hidden from me in plain sight this entire time? Maybe I should stop complaining about sig figs and uncertainty calculations...

  "Merci!" (Thank you!) Nurcan then leaves the Potions classroom.

  Most of the time, students only tended to think as far as the next test. On the other hand, Nurcan seems willing to "rock the boat", if you will. And dig deep she does. I don't get her kind too often, but when I do, it's a mixed bag, the potions prof reflects on the whole experience of dealing with Nurcan's complaint.

  Now that she knows the cold, hard truth about why these concepts she feels are key to learn potion-making are only taught much later, she keeps trucking on the review of the material for her remaining exams. Which, of course, she does with her roommates, who are all too willing to do so with her, so long as there's no arithmancy involved.