scientific notation ft. ghost

Everything made sense. Jesus, how had she not SEEN this!
The research, she realized - it had been screaming this in her face. All the clues had been there - and yet she'd been ignorant and didn't see them at all. And if what Mr. Evensman was saying was true..
Her eyes visibly brightened, as she noted down everything he'd said, sloppily, determined to draw a connection - and BAM, the connection was made. It all made sense. Some wonderful, twisted, stupid sense and she was going a million miles an hour, her mind was racing, and it all made sense!
"So, you are saying that since i have no business to linger for - that, that the business I had unfinished in life, to find a place to belong - since I found it here, with all of you... that means, that means that.. That.. OF COURSE! It all makes sense! Some strange frigging sense!"
She ran her hands through her messily-bunned hair, grinning almost crazily, like a mad scientist. Well, almost. She wasn't mad. She had the answer now!
Though, she hadn't been able to find it independently... which bothered her. She should have been able to find the connection on her own, solo. But that didn't matter, because she was finally able to make heads and tails of all her research. If she took the reason she was staying here into consideration, applied it to the context... YES! Aswan laughed... well, almost laugh-cried.... in relief. Everything. Made. Sense.
"Yes," she nodded vigorously, "yes, it makes sense now. Phew."
But... the matter of taking a physical object and possessing it... well, that would be a hassle. But to stay here?
It had to be done.
"If... If you would... I'd like to, erm, possess something temporarily, so as to not fade too much too soon. I don't suppose that would be too much to ask..? I mean, if not, I can always go to a jewelry store and look at pieces of jewelry.. I mean, you have already provided me with the answer - "

"Ashamed as I am to accept something.... well, accept help from others," she muttered, almost under her breath, "I'm afraid at this point I have n-no choice." Clearing her throat, she nodded. "Thank you. Er, f-for your help."
It happened all at once, to her, after she'd agreed. The teacher she'd met with gently placed his hand on a tome she'd only briefly noticed, and with a small but audible clap of energy (which never ceased to make her wonder - was it electric energy? Some form of magnetic frequency? Was there alchemy going on, like in a certain show she'd watched a few months ago? Was it arcane? She had no idea, but resolved to ask Mr. Evensman later), a tiny silvery bracelet, intricately etched with what she could only guess were ancient runes of some form (she would also ask Mr. Evensman about that later) appeared right underneath his palm.
Of course, interested as she was at how this gesture worked, she hesitated before reaching a hand to the bracelet, as if it were to bite her if she came close enough. After all, she was imposing herself on this teacher. It didn't feel right to take anything without a deal in place. His statement earlier, about seeking help and not feeling ashamed for it, was kind of alien to Aswan, who had found most answers herself most of her life. Nevertheless, he was right. Still... it didn't feel quite right.
"You are right about the help thing... Still, I feel it might be best if I can offer you something in return." Wait, that had just slipped out of her mouth! What was she saying? Well, maybe she could have taken up a bit more study, but -
Perhaps this could work. After all, he had given her a solution to her problem. It would not hurt to keep him in contact, lest she ever run into a problem again.
"Maybe it would be best if I enrolled in your class, taking on a few extra assignments, as compensation for this...?"
She pointed to the bracelet. "I mean, you wouldn't have to worry at all about my not having assignments turned in - I have all of my work done on time anyway, and work is kind of a hobby for me as well."

@Kaya

He was right of course. It felt like she had to compensate for something - he did just give her an out to her problem that she hadn't even realized was an out - but yes, he was a teacher. A true teacher's spirit, at that. Teaching not for money or for gains (like some other teacher's she'd known when she was alive), but for the sheer sharing of knowledge. Not out of punishment for not finding a solution either. It was then that Aswan took a step back to evaluate her actions. Why had she been like this lately? Much more "feeling" and sensitive than she usually would have been. More frazzled than she would have been. Where was that sense of pride she'd carried with her so often?
Hesitantly at first, then more resolutely, she took the bracelet from its place atop the book, slid it onto her wrist, and squeezed her eyes shut, trying to think of how exactly this worked.... until she felt a tiny little shock of... it felt like electricity? shoot through her wrist and made her fingertips tingle, as if she'd been zapped by lightning. Somehow, she felt much better than before. Much more awake. More vivid, more present... more relaxed. It was like she'd been restored to full HP. Whoa. It took a moment to adjust to - and she was so focused on this that she missed some of Mr. Evensman's speech. But he didn't have to know that, right? besides, she caught the gist - that the class was a place where her willingness to learn could soar.
She nodded, feeling better than ever, and pawed at the paper he'd slid across the desk to her, written in a dark ink. Understandable. To his merciless laugh, her counter was a fiercely sharp grin. "Oh, I think you underestimate my ability to be a perfectionist, sir. I have never failed a class. Not even in the college-level courses I'm taking. I am one of THE most motivated students you will find."
Looking back down at the rules, taking out her own dark-colored pen to note down, they went through the rules. Most of them, as Mr. Evensman had explained them, were straightforward and easy to follow (and if she was smart, she would avoid sleeping in class at all costs - by no means did she want to be sopping wet from a quick visit to the ocean. She'd had a good chuckle at the thought.) The only think that puzzled her was the blue-ink - and that was immediately explained by Mr. Evensman as well. Again, she stifled her chuckles. "Don't worry, I have more colors than just blue. A true pen connoisseur would, after all."
"Do you have any more questions for me tonight young lady Aswan?"
"Not at all. I look forward to being in your class." And for the first time in months, she felt truly confident.

@Kaya