That’s the only interpretation that even begins to make sense - if the decimal point actually indicates the division between two common (probably nested) units - currency being the most likely.
Still, 45.89 1/4 seems a bit too Hogwarts to be useful. 48.8925 is unambiguous.
The name of the book is “Contemporary Mathematics for Business and Consumers”. I can’t find what the original release date is, this book is the 6th edition. I could go along with it being used for money except there are problems in the book like 0.9 3/4. One thing I forgot to mention is that this is in the same section with percents.
My guess is that business types started doing this with fractions of a cent (and only fractions of a cent), and that they then showed the notation to the mathematician who was writing the book, and the mathematician then generalized the notation.
It’s pretty normal for trading. It usually means 1/4 cent, but not always - you just need to know your contract specs. Take a look here if you really want to see some weird units in trading.
Just to flesh out that last post, here is the description of the 10 year T-Note Future:
Why don’t they say one sixty-fourth?
Probably because before it only traded in 32nds, and later they decided they wanted to trade smaller increments, but they didn’t want to change the quote terms - perhaps because of existing contracts denominated in 32nds.
One thing that struck me, is that accountants and other financial types, are NOT necessarily mathematicians, and have historically evolved their own ways of dealing with numerical data (especially money or money-like data), sort of independently of the evolution of standard mathematical notation.
Case in point: Modern double-entry accounting, developed by Pacioli et al in the mid-1400’s and still used to this day. The concept of “negative numbers” was vaguely known to antiquity, but not well-developed until the 7th and 8th centuries. Thus, accounting developed the two-column system of Debits and Credits, using only positive numbers in both columns, to accomplish what they needed.
Today, with accounting handled by computers, debits and credits are handled with positive and negative numbers, yet in at least some software (I think) they are still presented to the user as positive numbers only, marked as Debits or Credits. In an introductory accounting class I took a few years ago, the only prerequisite was one semester of Algebra. So everybody should have known about negative numbers, but the few times it was mentioned for whatever reason, most of the class seemed to be lost.
If you want your students to understand algebra, you need trig or calculus as a prerequisite. An algebra prerequisite just means that they’ll probably be OK with arithmetic.
And 700 years wasn’t long enough for the accountants to learn negative numbers?
Please don’t lump accounting and finance together. We, at least on the finance side, hate that. While accounting doesn’t have much math, finance does, or can, depending on what type of finance you’re doing.
The basics: Capital asset pricing model - Wikipedia
intermediate: Black–Scholes model - Wikipedia
advanced: http://www.iam.uni-bonn.de/people/ankirchner/lectures/Goedecke_Uzelac.pdf
There are now quite a few programs that focus on quantatative finance: Home - NYU Courant
http://management.bu.edu/graduate/graduate-programs/msmf/?utm_source=finance%2Bbrochure&utm_medium=print&utm_campaign=Finance_brochure_Mathfn
For sure. I could tell you stories, but you’ve seen them all yourself too.
[Storytime!]
Introductory Statistics only requires one semester of algebra as prereq, as least when and where I took it. Yeah, right. Most of the class was mostly lost most of the time. With only 30-some seats and 60-some piling outside the door on the first day trying to get in, the instructor admitted them ALL, knowing full well that at most 30 would remain by Week 2. He was right. By end of semester, only 11 finished the class. I guess those were the ones who knew algebra. (As it happened, I had already completed math through DiffEq, so I knew at least what negative numbers were.)
In Introductory Econ, where you see all those odd graphs of supply/demand/price curves, etc. there was one graph on one page (forget what it was after all these years) that was clearly the derivative of a graph on another page. To me, that was obvious and meaningful. Nobody else had a clue.
In an Introductory Oceanography class, some mention was made of the highly negative (below-zero) temperatures at great depths. One older re-entry student asked what negative numbers were, requiring a 20-minute diversion to cover that. My father, a professor of History of Education, often complained that his students (graduate-level students!) often needed an explanation of why B.C. year numbering runs backward.
And yes, from my impressions of that Intro Accounting class I took: Accountants to this day don’t know what negative numbers are (unless, I suppose, some just happen to). But that whole semester of accounting, I don’t think negative numbers were ever mentioned.
We had one problem once: Given a fully-completed monthly balance sheet, but with one number deep in the middle of things left blank. Find the missing number. I made a simple algebraic equation (you had to, to keep straight of which numbers ultimately get added or subtracted to form the “bottom line”), solved for the missing number. I think I was the only one who got it. When I suggested in class to make an algebraic equation, the professor immediately shut me up. After class, he told me he did that because any mention of “algebra” would predictably scare the rest of the class away.
In a Intro Logic class, a similar thing happened. We did one chapter on Symbolic Logic, with all those symbols for logical operations, and parentheses, etc. – Someone in the class called it “hieroglyphics”. I pointed out that it was substantially similar to algebra. There too, the instructor shut me up, explaining likewise after class that it would scare everyone away.
[/Storytime!]
The COBOL computer language includes a display format specially to handle this, certainly; if I defined a field as PIC Z,ZZ9.99DB I would be telling the program “Four digits before the decimal, two after, suppress leading zeroes in the first three positions, insert a comma after the thousands digit if not zero-suppressed, append ‘DB’ if negative”.
Reference the OP, I’m 99 44/100 % sure I agree with the “dollars, cents, fractions of a cent” people. 