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Final Answers
© 2000-2015   Gérard P. Michon, Ph.D.

Using the  TI-36X Pro

A terrific little calculator,
possibly the best in its class 
(allowed on NCEES exams).

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Related articles on this site:

Related Links (Outside this Site)

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 |
education.ti.com :   TI-36X Pro overviewdatasheet  & guidebook.
How the short-lived TI-30X Pro Multiview (Sept.-Oct. 2010)  begat
the  TI-36X Pro  in March 2011  (by  Joerg Woerner,  DataMath).
Review of the TI-36X Pro  by  Edward W. Shore  (2011-04-17).
TI 36X Pro and wishes for a solar RPN calculatorEddie W. Shore  (2011-04-27).
Scientific Calculators and Diminishing Returns  by  Ben  (2011-09-16).
Texas Instruments TI-36X PRO Calculator  by  Nick Weil  (2012-01-12).
TI-36X Pro:  ZigZagBlog by  Joe  (2012-05-02).
Math Majeure  by  Rob Zimmerman  (2012-08-29).
Amazon customer reviews, including Charlie's review (2011-06-24).
TI Calculators  at  calculators.torensma.net  by  Elmer Torensma.
Texas-Instruments calculators  from the collection of  Tony Thimet.
HP 35:  The first electronic slide rule  by  Wlodek Mier-Jedrzejowicz, Ph.D.

Wikipedia :   Calculators   |   TI-36X Pro (2011)

Generalities :   How to use a Scientific Calculator  by  LearnersCloud.
Specific instructional videos for the  TI-36X Pro :
Solving a quartic equation,  by Eddie.
Standard deviation with TI-36X Pro,  by  Elmexico7.
Replacing the Battery  (CR2032 battery)  by  EngineeringUndergrad.

 TI-36X Pro calculator 
 by Texas Instruments

TI-36X Pro

Texas Instruments

solar power &
lithium battery
Dimensions :
(with cover)
width: 83.3 mm
length: 171.5 mm
(183.3 mm)
height: 15 mm
(18 mm)
weight: 116 g
(148 g)

41 keys + D-pad
dot-matrix LCD
96 by 31 pixels
4 lines of 16 characters
(5 by 7 font)
or 2D layout
13-digit precision
(10 digits shown)
8 variables: x,y,z,t,a,b,c,d
list price: $25
street price: $19
manufactured by Kinpo.

(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)
KeyMulti-tap 2nd
2nd 1st
mode quit
delete insert
ln(log(log  ( )  d/dx (_)|x=_
xyztabcd num-solv

 Come back later, we're
 still working on this one...

Videos :   How to Reset the Texas Instruments TI-36X Pro Calculator  by  Modyw94  (2012-09-28)
and   TI-36X PRO Programming Bug  by  Nick Weil  (2012-01-16).

(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).

 Come back later, we're
 still working on this one...

(2012-12-02)   Integer Arithmetic

To  factor into primes  an integer with  6 digits or less,  type  [math] [4] [enter].

 Come back later, we're
 still working on this one...

(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.

Thus, the  speed of light  (Einstein's constant, c)  is obtained by typing:

[ 2nd ]   [ constants ]   [ 1 ]

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 on  CODATA 2006.
Description & Symbol TI-36X Pro  ValueCODATA 2010Unit
Einstein's constantc1 299792458 299792458m/s
Normal gravityg2 9.80665 9.80665 N/kg
Planck's constanth3 6.62606896 10-34 6.62606957(29) 10-34J/Hz
Dirac's constant h-bar h / 2p 1.054571726(47) 10-34J.s/rad
Avogadro numberNA4 6.02214179 1023 6.02214129(27) 1023 1/mol
Ideal gas constantR5 8.314472 8.3144621(75)J/K/mol
Mass of the Electronme6 9.10938215 10-31 9.10938291(40) 10-31kg
Compton wavelength lc h / (me c) 2.4263102389(16) 10-12m
Mass of the Protonmp7 1.67262158 10-27 1.672621777(74) 10-27kg
Compton wl for proton lc,p h / (mp c) 1.32140985623(94) 10-15m
Mass of the Neutronmn8 1.67492721 10-27 1.674927351(74) 10-27kg
Compton wl for neutron lc,n h / (mn c) 1.3195909068(11) 10-15m
Mass of the Muonmm9 1.8835313 10-28 1.88353475(96) 10-28kg
Newton's constantG10 6.67428 10-11 6.67384(80) 10-11 N.m2/kg2
Faraday's constantF11 96485.3399 96485.3365(21)C/mol
Bohr radiusa012 5.29177209 10-11 5.2917721092(17) 10-11m
Classical electron radiusre13 2.81794029 10-15 2.8179403267(27) 10-15m
Boltzmann's constantk14 1.3806504 10-23 1.3806488(13) 10-23J/K
Stefan's constants 2 p5 k4 / (15 h3 c2 ) 5.670373(21) 10-8 W/m2/K4
1st radiation constantc1 2p h c 2 3.74177153(17) 10-16W.m2
2nd radiation constantc2 h c / k 1.4387770(13) 10-2m.K
Charge of a protone15 1.60217649 10-19 1.602176565(35) 10-19C
Atomic mass unitu16 1.66053878 10-27 1.660538921(73) 10-27kg
Normal Pressureatm17 101325 101325Pa
Standard Pressurebar  100000Pa
Ice point  =  0°Ct0  273.15K
Molar volume, 0°C, 1 barVm 273.15 R / 100000 0.022710953(21)m3/mol
Molar volume, 0°C, 1 atm 273.15 R / 101325 0.022413968(20)
Electric constante018 8.854187818 10-12 8.85418781762039 10-12 F/m
Magnetic constantm019 1.256637061 10-6 4p 10-7H/m
Coulomb const.  1 / 4pe020 8987551787 8987551787.3681764 m/F
Ampere constm0 / 4p  10-7 H/m
Z of vacuumZ0 m0 c 376.730313461770655468... W
a m0 c e2 / 2h 7.2973525698(24) 10-3  
1/a 2hce0 / e2 137.035999074(44)
Conductance quantumG0 2 e2/ h  =  4a / Z0 7.7480917346(25) 10-5 S
Rydberg's constantR¥ a / pa0  =  a2/ 2lc 10973731.568539(55)m-1
Hartree energyEh 2hc R¥  =  a2 me c2 4.35974434(19) 10-18J
Quantum of fluxF0 h / 2e 2.067833758(46) 10-15 Wb
Bohr magnetonmB e h / (4p me ) 9.27400968(20) 10-24J/T
Nuclear magnetonmN e h / (4p mp ) 5.05078353(11) 10-27J/T
Electron magn. momentme   -9.28476430(21) 10-24J/T
Proton magnetic momentmp   1.410606743(33) 10-26J/T
Neutron magn. momentmn   -9.6623647(23) 10-27J/T
Muon magnetic momentmm   -4.49044807(15) 10-26J/T
Gyromagnetic ratio
of the proton
gp    4p mp / h   267522200.5(63) rad/s/T
gp / 2p 2 mp / h   42.5774806(10) MHz/T

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...

Conversion Factors
Standard quantity TI-36X ProExact ValueUnit
Int'l  inch (1959)1 in01 2.542.54cm
Int'l  foot (12" = 12 in)1 ft03 0.30480.3048m
Int'l  yard (3' = 3 ft)1 yd05 0.91440.9144m
Gunter link (0.22 yd)7.92 in  20.1168cm
Gunter chain (22 yd)66 ft  20.1168m
furlong (220 yd)1 fur  201.168m
statute mile (8 fur)1 mi07 1.6093441.609344km
nautical mile (nmi)1 NM  1852m
acre1 acre09 4046.85642244046.8564224m2
Winchester gallongalUS11 3.7854117843.785411784L
fluid ounce1 fl oz 1 galUS / 12829.5735295625mL
Imperial gallongalUK15 4.546094.54609L
Imperial fluid ounce         1 galUK / 16028.4130625mL
ounce (avdp.)1 oz17 28.34952312528.349523125g
pound  =  16 oz1 lb19 0.45359240.45359237kg
grain  =  1 lb /70001 gn   64.79891mg
carat  =  1 g / 51 ct  200mg
troy ounce (480 gn)1 ozt  31.1034768g
Fahrenheit (°F)
vs. Celsius (°C)
°F21 (F+40)  =  1.8 (C+40)°C
Celsius (°C)
vs. Kelvin
t (°C)23 T   =   t + 273.15K
T (K)24°F
kilometer per hour1 km/h31 5/185/18 = 0.277777...m/s
meter per second1 m/s32 18/518/5  =  3.6km/h
knot  (NM/h)1 kt  463/900 = 0.514444...m/s
mile per hour1 mph  0.44704m/s
light-yearly33 9.460730473 1015 9460730472580800m
parsec1 pc35 3.085677581 1016 3.085677581491... 1016m
astronomical unit1 au (p / 648000)  pc 149597870700m
ångströmÅ37 10-1010-10m
normal pressure1 atm41 101325101325Pa
standard pressure1 bar  100000Pa
millimeter of mercury1 mmHg42 133.322387415133.322387415   Pa
Torr1 Torr1 atm / 760 133.322368421...Pa
kgf / cm2    98066.5Pa
lbf / in21 psi   6.89475729316836...kPa
kilowatt-hour1 kWh52 36000003.6 106J
IST calorie1 cal54 4.18684.1868J
15° calorie  4.1855 (3)J
calorie  4.184J
kilogrammeter  (kgf.m)1 kgm   9.80665J
erg1 erg   10-7J
horsepower1 hp55 0.7456998720.74569987158227022kW

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.

 Cassini 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... 1016 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 1016 m  (instead of the correct 13-digit value, which is now  3.085677581491 1016 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").

 Come back later, we're
 still working on this one...

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!

Videos :   Texas Instruments TI-36X PRO bug error  by  Mr. TechLabs  (2011-09-29)
TI Planet  (in French)  by  Critor   (2011-10-07).  In Europe, the calculator is called TI-30X Pro.
TI-36X PRO Programming Bug  by  Nick Weil  (2012-01-16).
Pseudo-Bugs:  Daniel Hendrycks (2012-05-06).

visits since December 5, 2012
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