Saturday, April 7, 2007

2.76E-3 is not scientific notation!

In Uncertain Principles' "Pick a Number" challenge, a pair of comments by a student used TI-83 notation to write mu_0 as 4piE-7 rather than 4pi x 10^{-7} (using pseudo-TeX due to the absence of superscripts and greek letters in this forum). This is an abomination perpetrated (in part) by math faculty at various levels, including at good old ICC.

It is bad enough when they tolerate using 3E-7 as if it conveyed the mathematical idea of exponentiation rather than the subtraction of 7 from three times the Erdos-Borwein constant E, but some will even tolerate 3e-7, when every child knows that this is seven less than 3 times Euler's (or Napier's) number e. [And, I might add, e is one of the most important numbers in mathematics, right up there with its friends pi, i, and -1. See my pi-Day observation posted back in March.] In my not so humble opinion, this is the equivalent of teaching BASIC in programming 1 to computer science majors.

It starts, of course, with the adoption of a particular graphing calculator (the TI-83 at ICC and elsewhere) that does not display numbers in correct scientific notation. It is reinforced when algebra instructors grade students on whether they correctly copy the exact contents of the display that results from carrying out a trained task (such as pointlessly using "trace" to "solve" an equation) in the prescribed fashion and never ask the student to also provide the correctly written value after rounding to, say, 3 significant figures. [Don't even get me started on whether they also look at any of the work the students have done, grading them on its correctness and clarity.]

Yes, computers and calculators often cannot handle data input of numbers in standard mathematical form, but that is no excuse for confusing expediency with correctness. Students must be taught to translate the expression shown by their calculator into the form used by all professionals in their published [*] work. They could also be told that much cheaper calculators, such as the Casio fx-115ms (for numerical integration and uber-cool symbolic prefixes in engineering mode) and many Sharp models, actually display a power of 10. For instructors, these other calculators also have the virtue of reducing cheating off of electronic formula sheets.

[*] Journals have, and probably still do, accept tables reproduced directly from computer printouts that use this FORTRAN format, but that is the exception that proves the rule.


Twice said...

This is a total pet peeve of mine too! I hate that!

Most of my students use calculators that do not use the "e" or "E" notation, but have the smaller raised numbers for the exponents. So they will write 7.4 x 10^2 as 7.4^2. This makes me want to pull out my hair!

My science majors do the E thing when they write down answers they got from Excel. Though they understand why it isn't right, they look at me in wonder that I care so much about it.

And in yet another case of banging my head against the wall, I have one student who claims her calculator has "issues". Actually, she just doesn't reliably put in scientific notation correctly.


Doctor Pion said...

I tell them that I care about it because it is wrong. And I take off a point every time I see it. That makes them care.

Your student with "issues" might be confusing *10^x with the EE key, and not realize that one is multiplication and the other is a single number.

Twice said...

I also do this. (take off points) I think perhaps I come across like I think it is a personal insight. One of the perils of pet peeves for me - I'm very bad at hiding my frustration.

Yes, my non-majors always confuse the 10^x key with the EE button. Now it does not bother me so much because I just address it in class all at once, and have finally figured out how to trick them into paying attention.

My senior student, however, just routinely forgets +/- key -or- forgets the exponent all together -or- enters the exponent as the number. On the plus side, she's very nice and is surprisingly good in lab.

Doctor Pion said...

You should blog about how you get them to pay attention. I'm interested.

And I come across like it is my insight, no apology needed there. Just wait until I find the time to write about algebra classes that only do y(x) and never P(V) or log of this vs sqrt of that (like is seen lab analysis). That common peeve drives the chemist in the office next door absolutely nuts.

Dan said...

I must take the alternative view; the goal is efficient communication and a number written in E notation is more compact and much easier to type and to read. I think it should be made an acceptable standard format.

Doctor Pion said...

My complaint starts with when it is hand written. That begins to suggest the student doesn't even know what it means.

It is only easier to type in an ASCII format like e-mail, and even then you need to ensure that your reader knows your statement about 3.00e-7 does not refer to e = 2.71828.... In other formats, such as TeX, it takes only a second longer to write it correctly.

If you are just being lazy, use the correct SI prefix. It has the advantages that it is compact, unambiguous, and a display option with the better calculators.

Anonymous said...

Frankly, I find the assertion that no person should ever express 1*10^6 as 1E6 at best childish and at worst an invitation for error. Confuse the E with the "ErdÅ‘s–Borwein constant," are you kidding me? I'm a nuclear engineer, and not many of my coworkers have experienced that particular issue despite crunching numbers on a pretty professional basis.

The issue I AM concerned about is mistyping 1*10^6 as 1(10^6, 1&20^6, etc. 1E6, it's three characters, you don't have to use the shift key and poke at the asterisk key, etc etc. Run the probabilistic risk assessment, whatever, you aren't going to make as many mistakes and it's more compact, and that's why I like it. Languages change, maybe it's time to adopt E notation in the mathematical thesaurus?

But hey, don't get me wrong, I love my math classes and professors, and you guys get to rip me to pieces when I write an ill-posed problem or a crummy advection/diffusion code. But when you're teaching non-majors, how about some common sense? "Hey, this is usually confined to calculators, most people will understand what you're talking about but it's not strictly correct so you better know your audience." Besides,they probably won't remember what scientific notation is in 5 years so it'll be a moot point.

Doctor Pion said...

I am not teaching non-majors, but even non-majors need to know the difference between a billion and a trillion.

I am teaching wannabe engineers, many of whom appear to have taken math classes from people who only want them to copy down what their calculator displays without knowing what it means, let alone whether all of the digits are significant. (In particular, they don't seem to know that e is a number and not a letter.) Some also cannot solve an equation without graphing it.

And since they are writing the answer to a problem on an exam, I expect them to write it like they know what it means.

Dan said...

Part of the difficulty with the traditional form of scientific notation is the need for a multiplicaiton operator between the mantissa and the 10, when the rest of an equation, which can be quite complex, doesn't have multiplication operators. If I add an X for times, is it a variable? If a star, why only in that one spot? Unless stras are used between all products there is no consistent terminology. I really think what Wikipedia refers to as scientific E notation is a simpler and more easily understood alternative. The capital E certainly is used millions of times more often to mean "move the decimal point" than for any other meaning, and it just saves time.


Dan Woodard, MD

Doctor Pion said...

The fact that there is a multiplication sign in a number written in scientific notation is not a problem, it is a feature. If you don't like it, use the SI prefixes. That is what I would expect a physicist, engineer, and - in particular - physician to do. It saves even more time, not to mention lives, and some calculators will even display those prefixes for you.

The capital letter E is used to denote energy. It is an algebraic variable that is commonly used in all scientific work - particularly in physics and engineering. The fact that students come to me more comfortable with misusing a calculator to manipulate numbers inaccurately does not excuse them from using the tools of algebra. And if you do that, there is never any reason to put a number in scientific notation in an algebraic expression. You work with symbols, one of which might have a value that requires scientific notation.

Finally, Wikipedia is not an authority. In this case it is incorrect. That particular notation was required by the primitive computing interfaces we no longer use.