This chapter was more for me to vent over math being difficult back in high school. (Look at me now; I'm studying to become an engineer :P)
This whole exchange was in inspired by one of the math teachers trying to help me with a particular question, and they kept doing the same mistake over and over again. And I'm thinking if my math teacher made that mistake after 10+ years of teaching math, Warner could do the same.
And I'm sorry if the equations are hard to follow in the text.
"What do you want?", Warner asked as he saw Alice standing in the doorway to his office. She had a notepad and a thicker book bundled in her arms. She looked like she was about to start her homework.
She didn't have any business doing it in there.
"Are you busy?", she asked. Shifting in her posture to move the weight in her arms.
"Not really", he said, turning his attention to the finished paperwork in front of him. Starting to put them in different file holders.
"Why do you ask?", he continue.
"I want to sit in here while I do my math homework", she answered.
When he looked up in question she explained:
"It's way more quiet in here, and Delalieu is busy so he can't help me if I get stuck."
"How nice of you to just assume that I'm willing to help you", Warner remarked.
Alice shrugged.
"Well, you said you weren't busy, so what's the problem? And I don't need constant help. It's just percent", she replied, though it was clear that she was still waiting for a formal invitation to the table. She was bouncing her weight on the balls of her feet.
Warner sighed.
"Only if you promise to be quiet", he said and waved for the empty room on the table in front of him.
"I promise!", she assured and made a skip towards the table. But before she could take a seat at the far end he interrupted her.
"You can sit over here so I can look at what you're doing", he said and gestured for the empty spot right in front of his desk.
She gave him a suspicious look. Narrowing her eyes at him.
"What?", he demanded.
It was remarkable how easily she could annoy him.
"Don't you trust me?", she asked.
"Why on earth would I trust you with anything? You showed up in my office one day!", he snapped.
"But what does that have to do with anything?", he then asked to get some clarification.
"Only time people watch you do work is because they don't trust you to actually do it…", she explained. Still with the look of suspicion.
"Just get over here", he ordered.
She sat there and worked for about twenty minutes with Warner giving her calculations a glance every few minutes. She didn't understand why he did it though, since all he saw was upside down numbers, but she didn't say anything.
Though after a while he started scowling in confusion when he looked it over.
"What are you doing?", he asked leaning forward and cocking his head to see better.
All he saw was some kind of small decimal being repeated over and over again.
"It's permille", she answered.
"Or parts-per-million…", she said suddenly unsure.
Warner blinked a few times.
"You don't know the difference?", he asked.
Alice frowned.
"Well, we just went through it…", she protested as Warner got up to move over.
"Well, the math is faster now than when I was your age. We didn't go through this until high school."
"Why would they speed it up?", she muttered.
"In Asia the children did just fine. The reestablishment promised a higher educational standard, so this is what happened."
"Can't you just slow it down again? You're the boss here", she said.
"That's not how it works", Warner said curtly.
He sat down in the chair next to hers and pulled over her notepad. He flipped the page to a clean one then he held out a hand expecting her to hand him a pencil.
She did after some stubborn glaring.
"So", he started,"You know about percent, right?", he asked drawing the symbol at the top of the page.
"Mhm", she nodded. Resting her chin on her knuckle.
"Well, did you know per-cent means per hundred? Cent being a hundred in latin."
"One percent equals a hundredth", he clarified, writing the zero point zero one. While Alice muttered 'I already know that…'
"Well, did you know the sign represents a hundred as well?", he asked. Tapping the tip of the pencil at the sign.
"That's the one", he tapped the diagonal middle part,"And those are the zeros", he said pointing at the circles.
"Huh?!", Alice said. Leaning forwards to see.
As the information clicked she let out a small breath.
"I did not know that…", she confessed.
He felt a smug smile tug at the corner of his lips.
"In that sense permille does the same thing. Per-mille is per thousand", he explained as he wrote up the same things as before. But with extra zero's. Zero point zero zero one.
"One permille equals a thousandth. And it's the same with the sign. It's just an extra zero."
"Huh", she said. Her tone amazed.
"Now about parts-per-million. Do you know how many zero's there are in a million?", he asked.
She had to change her mind twice before answering, after counting on her fingers.
"Five!", she proudly announced.
"It's six!", he snapped poking her on the forehead with the pencil.
"Ow!"
He then explained that since it was a millionth there was zero point "five zeros" before the ones digits.
"So 6 ppm is written zero point zero zero zero zero zero six", he explained while he neatly wrote up all the numbers in their boxes.
Then he also explained how 60 ppm and 600 ppm required less and less zeros. And how it had to do with moving the coma left and right.
It took ten minutes all in all.
"Now to how to use it", Warner announced.
"Can't we take a break?", Alice asked.
"My brain hurts…"
"It's not like you've done anything yet!", Warner reminded.
"Which one was it that you were doing before?", he asked.
Alice pointed at one of the later questions.
"That one."
'What is 70 ppm of 400'000kg?'
"The easiest thing to do is writing them in scientific notation. Do you know what that is?", Warner asked, flipping to another clean page, then pushed it over the table top for Alice to do some writing.
"It's the tens with exponents, right?", Alice answered as she took the pencil from him.
"Right", Warner said.
She wrote "70*10^-6 times 4*10^5".
And after some tinkering she got 280*10^-1 = 28kg
"Is it right?", she asked as Warner took the paper.
"Well the answer is right…", Warner said as he looked it over,"...but if you want better grades you're supposed to use scientific notation properly."
"What?", Alice asked, very offended.
"You can't use seventy, you have to divide it by ten to get seven first", Warner explained, taking the pencil,"Which changes the exponent by?"
"You move the comma another step", Alice answered after some thinking.
"Right, so it's seven times ten to the power of negative seven, times four times ten to the power of five", Warner said writing everything down. ((7*10^-7)*(4*10^5))
"Which gives us... zero point twenty eight...?"
He stared at it for a while. Tapped the pencil against the table.
"That's not right…", he muttered.
"What did you do wrong?", Alice asked, leaning forward to see.
"I don't know…"
He redid it and counted the zeros.
And redid it again.
And again.
And again.
Crossing out the failed attempt every time.
"Aaron, can't we just get a calculator?", Alice huffed, arms folded on the table and her chin resting on her arms.
"No", he snapped, then counting the zeros under his breath.
It was still not the right answer.
He drew a line over the equation.
Wrote it up again.
"And then you move the comma", he instructed to no one.
"Aaroooon", Alice whined, muffled by her face against her arms.
He paid her no mind.
He tried a few more times, then suddenly in the middle of writing his zeros he went rigid.
He crossed out everything he had done up to that point. Ever so collected. Then flipped the book to a clean page.
"What?", Alice asked as he wrote it up on last time.
He didn't answer.
When he was finished he tore out the previous page; covered in crossed out zeros, crumbled it in his hands and then stood up.
Alice looked at the page saw that "(7*10^-5)*(4*10^5) = 28" was neatly written at the top of the page, then circled.
"Why did you write seven before?", she asked.
"I didn't", Warner replied, back facing her.
"Yes you did. You got zero point twentyeight…", she reminded.
"You don't have any evidence of that", he answered curtly and tossed the crumpled paper in the wastecan.