NCEES-Approved Calculators:
Casio FX-115 series, HP-33s and HP-35s, TI-30X and TI-36X series.
A few misguided instructors are still disallowing the TI-36X Pro for their own exams,
possibly because they thought the "Pro" suffix meant "programmable" (well, it doesn't): |
Chemistry 111A at WU, Fall 2012 |
(2012-11-30)
Basic keys and modifiers. Shifted keys and multi-taps.
Most keys have more than one use. Introducing multi-tap.
The key labeled "clear" (top-right corner, below the prominent
4-way navigation button) is used to recover from errors and/or clear the screen.
Yet, the "clear" key by itself doesn't invalidate changes made in the setup screen
(which is accessed via the "mode" key, at the top left of the keypad) or any
other menu that allows multiple changes.
To clear the calculator's memory and return it a pristine condition with all its factory settings
(including angles in degrees) you may push the "on" and "clear" key simultaneously.
This has the same effect as the full "reset" obtained by punching in
"2nd", "0" and then "2" (for "yes").
The "delete" key at the middle of the top row is far less drastic, as it deletes one
element at a time (usually the last one entered but you may also
target something else with the navigation button).
On basic calculators, every key has a single use.
This wouldn't be practical for calculators that offer many functions.
Advanced calculators often feature several modifiers keys (shift-keys)
that allow access to multiple functionalities for regular keys.
The TI-36X Pro only has one such
shift-key (colored blue and labeled "2nd" at the top-left corner of the keyboard).
Yet, this calculator offers a lot of functionality by taking advantage of the
multi-tap
approach which is so popular for alphabetic entry on telephone keypads:
To obtain the different meanings of a key, just press it several times...
The calculator doesn't have to impose any time limit between the taps because
it's designed so that there is never a need to use
different meanings of the same key twice in a row.
(Well, this means that you must enter
i*p
instead of ip, even
if you find the latter more elegant.)
The double-tap method is clearly superior to a separate shift key for single-finger
operation of a keypad (every key acts as a shift-key for itself, so to speak,
without a journey across the keypad).
Other calculator designers have been wasting at least one shift-key by
forsaking multi-tap.
The designers of the TI-36X Pro may have overused this by cramming
all of its 8 variables (x,y,z,t,a,b,c,d)
on a single key, which you must press 8 times to access "d".
The functions of the 41 keys (besides the quad-navigation button)
(2012-12-02) Decimal numbers, fractions and mixed fractions.
Toggling between representations with the key above the "enter" key.
If you didn't attend elementary school in the US or the UK, you may be puzzled
by the so-called mixed fraction representation of
positive rationals:
The integral part is followed by the "fractional part"
(a positive fraction less than one) without any sign between them
("+" is implied, which is an unfortunate exception to the international
implicit multiplication rule which says
that the mere juxtaposition of two well-formed expressions denotes their product).
To input a number a a mixed fraction on the TI-36X Pro,
press [2nd][7] and you'll be prompted
for the three relevant integers in 2-dimensional edit mode
(integral part, numerator and denominator of the fractional part).
Supplying anything but integers will trigger a SYNTAX ERROR.
If a negative sign is given before the integral sign, the whole thing is negated
(not just the integral part).
(2012-12-02) Integer Arithmetic
To factor into primes
an integer with 6 digits or less, type [math] [4] [enter].
(2012-11-30) The 20 built-in physical constants of the
TI-36X Pro
The SI values of the first nine are available in just three keystrokes.
The menu that pops up after the first two keystrokes serves as a reminder of what constant
is associated with which numeric button
(1-9 only, the "0" key is unused).
The menu may also be navigated to
hightlight the description of a constant whose SI value can then be fetched by pushing the usual
[enter] key (bottom-right corner of the keypad).
That latter access is mandatory for 11 of the 20 predefined constants.
In the following table, we've given every constant known to the TI-36X Pro
an ID from 1 to 20 according to the order of its appearance in the calculator's menu
(which only shows IDs below 10).
For good measure, we've also listed other physical constants of
some importance which have been similarly featured by other calculator manufacturers
(or should have).
The standard convention
(discussed elsewhere on this site)
is that the digits between parentheses that follow
a measured quantity indicate its experimental uncertainty (one standard deviation)
expressed in units of the least significant digit.
The 20 predefined constants of the TI-36X Pro are based onCODATA 2006.
The TI-36X Pro has an internal accuracy of 13 digits,
but never displays more than 10 digits.
We've followed that convention in the above table, occasionally showing
fewer decimals than internally stored.
For clarity, the calculator displays answers with at least a two-space indentation on
its regular 16-character line.
With two formatting characters (the decimal point and the exponent sign)
and a two-digit exponent, there's still enough room to display 10 digits,
unless the number itself and/or its exponent sport negative signs, in which case
the value must be shown rounded
to 8 or 9 significant digits.
The green highlighting
in the above table indicates exact constants that have been
stored internally at the full nominal 13-digit accuracy of this calculator
(and correctly rounded at that internal accuracy,
kudos to the Texas Instruments engineers for not being sloppy on that one).
Consider, for example, the value listed above with ten decimals (8.854187818) for the
value of the electric constant (a.k.a. the permittivity of the vacuum).
Its SI value is known exactly because of the modern definitions of the
meter and the ampere.
Yet, as it involves a two-digit negative exponent (E-12)
the display is rounded to 9 digits (8.85418782).
If you multiply that by 1E21 you obtain what appears
to be a ten-digit integer (8854187818) but when you subtract
8854187817 from it (keyed in manually) you obtain 0.62 (actually 0.620)
which reveals the (correct) 13-digit internal representation of that constant:
8.854187817620 10^{-12}
Likewise, inside the TI-36X Pro,
Coulomb's constant is 8987551787.368
and the magnetic constant is
1.256637061436 10^{-6},
with 13 correct digits.
(2012-11-30) 20 pairs of unit conversions
Unlike most calculators, the TI-36X Pro has no conversion glitches.
In the following table, the 40 conversions (20 reciprocal pairs)
offered by the TI-36X Pro are given a 2-digit ID.
The first digit (1-5) is the number of the submenu of the "convert"
menu where that conversion appears. The second digit is its rank within
that submenu (with the exception of the items numbered from 01 to 20,
which are all in the first submenu.)
With the only exception of the two conversion pairs
involving the joule (J)
in the fifth submenu, the mnemonic rule is that:
Odd-numbered conversions (appearing in the left column of submenus)
translate non-metric units into metric ones_{ } (usually SI units).
Even-numbered conversions^{ } (appearing in the right column of submenus)
translate metric units into something else.
To apply this rule, understand that (for instance)
kelvins (K) and meters per second (m/s)
are, so to speak, more metric than,
respectively, degrees Celsius (°C) and kilometers per hour (km/h).
I view as a minor bug the violation of this pattern
for the two pairs of conversions involving the joule (J)
in the fifth conversion screen ("power & energy")
where conversions to J should appear in the
left column.
The calculator allows you to conjure up a conversion submenu by number
(the first digit in the ID, if nonzero) but won't let you execute a specific conversion
by using its rank within the submenu (the ID itself or its second digit if 21 or more).
It would greatly improve the functionality of the calculator for routine
computations if it did (in a future version of the TI-36X Pro, maybe).
That way, someone who regularly uses a specific conversion could
simply memorize its code to execute it very quickly.
For example, since conversion from pascals to atmospheres is the second
item in the fourth submenu, one could conjure it up by punching
2nd-8-4-2. Right now, all you can do is punch
2nd-8-4 to get to the proper submenu, then navigate and select...
Kudos to the TI engineers for getting all of the above conversion factors right
at the 13-digit internal precision of their machine
(especially the numbers
highlighted in green
which are often butchered by others).
Of course, I can only regret that they followed the lead of other
calculator manufacturers in perpetuating the
dubious IST conversion
factor for the calorie (which is merely derived
from the final definition of the Btu, a unit unknown outside the US or UK).
The scientific community has been using the 4.184 J/cal
conversion factor since 1935.
Since August 2012, the astronomical unit of length (au)
has an exact metric equivalent.
Since it's defined as a precise multiple of the astronomical unit,
the parsec (pc) too has a freshly minted
final equivalent in metric terms which may differ slightly
from previous experimental conversion factors (which are now obsolete). We now have:
1 au = 149597870700 m (by definition)
1 pc = 648000 au / p =
3.0856775814913672789... 10^{16} m
Those conversion factors were enacted so recently that no calculator
can be expected to be up-to-date now (and for some time to come).
Indeed, the TI-36X Pro actually uses for the parsec a slight 11-digit overshoot
of 3.085677581200 10^{16} m
(instead of the correct 13-digit value, which is now 3.085677581491 10^{16} m).
Multiplying this into p / 648000
would give the following approximation for the astronomical unit:
149597870685.8741...
(or 149597870685.9 if rounded to 13 digits)
The (outdated) source of
that precise number is a mystery to me.
(2012-11-30)
Gripes & Bugs
From debatable or objectionable features to minor flaws or severe ones.
Gripes :
You can only enter the negative sign of a number before the rest of it.
The calculator won't even try to factor an integer of more than 6 digits.
The proper conversion factor should be used: 4.184 J to the calorie.
Broken Pattern:
In every pair of unit conversions, the conversion to
the "more metric" unit is first (left column) except for the joule (J).
The symbol of the kelvin
(SI unit of temperature) is K (not "°K").
Bugs :
To the best of my knowledge, the bug reported elsewhere in September 2011
(about a bad display of multiples of
p in "mixed fraction" format)
has not been fixed yet. It's still on the calculator I bought in November 2012.
The issue is strictly a display problem which you'll never notice if you keep
the factory setting which makes the calculator display any rational number as a
plain fraction (the ratio of two integers, which may exceed unity).
Even if there was no bug, I'd recommend that you keep it that way.
(Never use option "1" on the "math" menu. If you ever do,
press "on" and "clear" simultaneously to clear the calculator's memory and
tell it, litterally, to forget about mixed fractions.)
If you've not been raised in the US (or, I presume, the UK)
you may need to be told that a so-called mixed fraction
is what you get when you omit the "+" sign in the sum of a positive integer
and a positive fraction below unity.
In some countries (including the US) children are indeed taught that
this sign is optional.
That enables them to read tables and labels where this "convention" is
traditionally used (mostly in connection with nonmetric units).
That would be fine if people were not also taught that this usage is more or
less mandatory, that the "+" sign (which makes everything clear
in an international context) is somehow not cool
and/or that a fraction whose numerator exceed its denominator
(a so-called improper fraction)
is a bad citizen.
I beg to differ on all counts.
By all means, do teach children to
decipher the intended meaning of mixed fraction but, please,
don't force them to use those things.
Also, do tell them that mixed fractions cannot be used within
mathematical expressions unless surrounded by parentheses.
The aforementioned bug is very well described in the
blog
of Nick Weil (2012-01-17).
I recommend that you read Nick's prose rather than just watch the video(s) about the bug.
I also recommend that you avoid mixed fractions in any scientific work,
with or without the TI-36X Pro calculator!