LCD: 96 by 31 dot matrix + annunciators
Normal font: 5 by 7 (4 lines of 16)
Menu font: 5 by 6 (eight 5/6 char. labels)
Small font: 4 by 6 (e.g., exponents)
Matrix computations up to 3 by 3
Numerical integration and differentiation
Handles fractions and decimal overbar
No programmation, graphing or CAS
LCD: 192 by 63 dot matrix + annunciators
Normal font: 9 by 14 (4 lines of 17)
Small font: 5 by 9 (6 lines of 32)
Annunciator for solar power (991EX)
Matrix computations up to 4 by 4
Numerical integration and differentiation
Handles fractions and decimal overbar
No programmation, graphing or CAS
"552 functions" advertised (no GCD
)
Constants & unit conversions via menus
Tabulates 2 formulas at once
Spreadsheet (5 columns & 45 rows)
Displays QR codes for smartphones
92.2 g (127.8 g)
80 x 162 x 13 mm (83.5 x 164 x 15.6)
Weight with LR44 battery (and cover)
Dimensions (with cover)
93.5. g (130.5 g)
76.8 x 165 x 12 mm (81.5 x 167 x 17.3)
(2015-12-03) Casio's EX Series of Scientific Calculators
Hardware improvement over the ES Series, at a higher cost.
Released in the Spring of 2015, the Casio fx-991EX (above right) improves in
speed and screen resolution over its predecessors of the ES series.
A larger memory allows a greater functionality in the EX series
(4 by 4 matrices are now supported, instead of 3 by 3 for ES calculators)
and a slightly better precision (1 more digit).
However, some beloved functions have been dropped:
The GCD function is absent from the fx-991EX (552 functions) but
survives in the German
fx-991 DE X (696 functions).
Besides a more intuitive interface and the support of "engineering
symbols" (prefixes)
there are two noteworthy innovations: Spreadsheet calculations and the
generation of QR graphics readable by smartphones.
(2012-10-08) Casio's ES Series of Educational Scientific Calculators
Many features, without graphing or programmation, for less than $20.
Although outdated calculators in the Casio ES series are still available,
Casio is mostly marketing one calculator powered in two different ways:
The fx 570es is powered by one AAA (R03) battery
which would last for about two years (17000 hours) if the calculator
was just left "on", displaying a flashing cursor.
The other version comes with "dual power": a solar cell backed up by
one small LR44 (GPA76) button battery, which is good for no more than 3 years.
That model is labeled either fx 991es (in Europe)
or fx 115es (in North America).
Those calculators have been advertised as featuring "403 functions".
Their upgraded "PLUS" versions (2012) offer "417 functions".
Such calculators are best viewed as several specialized calculators combined
into one unit. The specialization is determined by the number of the "mode" selected
in response to the menu that pops up
when you hit the MODE key (located at the top right of the keypad, next to the
ON button). The choice for normal computation is 1.
The
downgraded
calculators of the series, which are advertised to offer "249 functions"
(fx-82es, fx-83-es, fx-85-es, fx-300es and fx-350es) offer only 3 modes.
So do the slightly better "252 functions" fx-82es Plus, fx-85es Plus
and fx-350es Plus:
1:COMP 2:STAT
3:TABLE
The fx-95es Plus has "274 functions" and a menu with 6 modes:
1:COMP 2:STAT
3:EQN 4:TABLE
5:INEQ 6:RATIO
The standard "403 functions" versions the fx-115es, fx-991-es or fx-570es have 8 modes:
The PLUS version ("417 functions") of those same calculators flaunt three additional choices
(for a grand total of 11 modes) that appear
on an extra menu that comes up from the aforementioned main MODE menu
when you press the lower part of the big round
navigation button:
1:INEQ 2:VERIF
3:DIST
(2012-11-09) MODE 1: Ordinary Computations
The Basics.
(2012-10-08) MODE 4: Base-N Integer Arithmetic
In radix ten (DEC) sixteen (HEX) two (BIN) or eight (OCT).
At a time of my life when I was doing assembly
programming daily, I once spent a lot of money on a specialized
calculator that was doing only that!
To switch between bases, use the four keys at the left of the third row, which
are clearly labeled in blue for
DECimal, HEXadecimal, BINary and OCTal.
For the upper hexadecimal digits A,B,C,D,E,F
use the keys of the fourth rowm that are so labeled (in red).
The display shows the current computation on the first line,
the radix (Dec, Hex, Bin, Oct) on the second and
the (last) result on the third line.
The basic functionality of the calculator is available for integer
arithmetic this way (including STO, RCL, M+ and M-).
Division is performed by discarding the remainder if there's any.
Negative results are understood to be
in two's complement
with a 32-bit word-size. They are shown with a negative sign in
decimal or binary
but are displayed "raw" in hexadecimal or octal (where the
negative of 1 is, respectively FFFFFFFF and 37777777777).
In other word, arithmetic is performed
modulo the thirty-second power of two.
Two capitalized bitwise unary operators (Not, Neg) and four lowercase
bitwise binary operators (and, or, xor, xnor) are provided
in the specific menu that pops up when taping Shift-3 in this mode.
(2012-10-09) MODE 6: Matrix Manipulations (dimension 3 or less)
Three special variables have values that are matrices: MatA, MatB, MatC
This is clearly for educational purposes only.
The matrices are cleared when you switch modes and you cannot do anything
with the results. Matrix elements can only be real numbers
(complex values are not allowed).
(2012-11-24) MODE 7: Tabulate a function (or a pair of functions).
You are prompted for an expression for f (x) and g (x).
(Press "=" when prompted for g if you only want to tabulate one function.)
Then you're asked for a starting value of x, an ending value and an incremental step.
The classic version of this calculator only allowed
one function to be tabulated at a time.
If that's all you want from your "plus" calculator,
you can avoid any prompting for "g" via the
option labeled "5: TABLE" in the second
screenful of the SETUP menu (to access that,
press Shift-SETUP, next to the ON button,
followed by a down arrow from the big round navigation button).
What will be displayed as a result is a table with 3 or 4 columns, showing
a line number, a value of x and the corresponding values of
f (x) and (possibly) g (x).
Use the navigation button, down or up, to view many lines.
Tutorial Videos:
Graphing Functions
with the Casio fx-115 ES (not "plus" in this demo).
(2012-10-25) CALC : Repeated Calculations
Work out a formula for many values of the input variables.
(2012-10-19) CONST : Fundamental Scientific Constants
Numerical values of 40 physical constants, in SI units.
Calculators in the Casio ES series provide the values (in SI units)
of 40 physical constants.
Those are obtained via the CONST key (Shift-7)
followed, as prompted, by a two-digit identifier from 01 to 40
(according to the menu printed inside the calculator's protective cover).
This combination of
3½ keystrokes results in a symbol that can be evaluated by itself or
as part of any algebraic expression.
As of this writing, the "fx-115es Plus" uses the
latest (2010) self-consistent values of physical constants recommended by CODATA.
The links to the NIST database provided below may show slightly different values
after 2015 or so (the CODATA recommendations are regularly
revised with a periodicity of about 4 years and the new values become widely available in the
second part of the year following the nominal date).
The values of a few physical quantities are khown exactly de jure
because of the way modern units are defined (for example, the speed of light
is exactly
299792458 m/s by virtue of the SI definition of the meter).
Otherwise, the most precisely known physical quantity
is the following dimensionless ratio, expressing the value of the
magnetic moment of the electron
using the Bohr magneton as a unit.
The standard convention used here
is that the digits between parentheses at the end of
a measured quantity indicate its experimental uncertainty (one standard deviation)
expressed in units of the least significant digit.
The yellow highlighting
for the electric constant indicates that the built-in fx 115es value
should have been rounded up to
8.854187818 pF/m.
We have similarly highlighted Casio's dubious choice of the symbol c0
instead of c for the speed of light in a vacuum
(Einstein's constant)
which they obscurely grouped with the historical radiation constants.
The Casio engineers may have been afraid of a possible confusion with the variable "C",
although they do display the latter in UPPER case.
Faced with the same dilemma, competing manufacturers simply
made sure to use a smaller font for Einstein's constant than for the names of variables
(which those other folks display in lower case, by the way).
That's a much better solution than Casio's artificial subscript which nobody else ever uses
(especially in calculators intended to contribute to the educational experiences of their users).
Arnold Sommerfeld's
fine-structure constant
(a) is the only listed
constant to be dimensionless. Its numerical value would be the same
in any coherent system of physical units and it remains a mystery:
a =
m0 c e2 / 2h =
e2 / 2hce0 =
1 / 137.035999...
The following lengths form a geometric progression of common ratio
a :
1 / 2R¥
2p a0
lc
2p re
That's the first of many noteworthy relations between the above constants:
Electron Magnetic Moment (in Bohr Magnetons) and Fine Structure Constant
by David Hanneke, S. Fogwell, Gerald Gabrielse
g/2 = 1.00115965218073(28)
and a = 1 / 137.035999084(51)
(2008)
Precision tests of QED
(2012-10-19) CONV : Physical Units and Conversion Factors
40 predefined unit conversions (a few inaccuracies and one mistake).
Calculators in the ES series don't allow physical dimensions to be attached to
numbers (it's a delicate issue even for top-notch calculators by
HP or TI).
What they do is provide the ability to perform 40 predefined unit conversions.
Those are obtained via the CONV key (Shift-8)
followed, as prompted, by a two-digit identifier from 01 to 40
(according to the menu printed inside the calculator's protective cover).
Regrettably, some of Casio's conversion factors differ from the precise
legally enacted values.
In the table below, we have highlighted in yellow slightly inaccurate
conversion factors which should have been stored with full precision
(or, at least, better accuracy) given the capabilities of the calculator.
Highlighted in red is a plain mistake (Casio uses a deprecated value for
the "15° calorie" instead of the proper thermochemical conversion
factor for published data involving calories).
Only the conversion factors that can be specified exactly with
finitely many decimals are tabulated below (for the unlisted reciprocal conversions,
usually corresponding to even indices, exact conversion factors
would entail repeating decimals or fractions).
The most obvious nontrivial ommission is the
pound-force (lbf)
whose lack of conversion by NASA once caused a costly probe to
crash on Mars:
1 lbf = (0.45359237 kg) (9.80665 N/kg) = 4.4482216152605 N
Also missing is the British thermal unit (Btu) whose
official IST value is:
1 Btu = (0.45359237 kg) (2326 J/kg) = 1055.05585262 J
With the sole exception of the last pair of conversions
(between calories and joules, with an erroneous conversion factor)
the rule is:
Odd-numbered conversions translate non-metric units into metric ones.
Even-numbered conversions translate metric units into something else.
According to Casio's documentation [2015 user's guide for the fx-991EX]
their questionable conversion factor for the calorie
is intended for "values at a temperature of 15°C".
Actually they chose an outdated value which is rarely retained, although it
appears on page 551 of The Encyclopedia of Physics
by Robert M. Besancon (1966, 1974, 1985, 1990).
It's also what gives the dubiously rounded value of
105480400 J (100000 59°F-Btu)
still quoted commercially. Worthless in a scientific context.
This dubious choice may have been
influenced by competing definitions of the calorie.
It's just one digit off from the IST "definition" which led to another mistake (perpetuated
by other calculator manufacturers for thirty years). The bogus IST conversion factor of
4.1868 J/cal, which did appear in a few misguided publications,
is ultimately just an offshoot of the unrelated definition of the Btu
(unused in modern science and unknown in most parts of the World).
Since 1935, the scientific community has used almost exclusively the
thermochemical conventional definition of
exactly 4.184 J
to the calorie, for all results published in calories.
The numbers highlighted in yellow
are needlessly inaccurate (but not nearly as bad as what we just discussed).
Let's give just one example:
1000 mmHg is the pressure felt at unit depth (1 m) in a liquid having the
conventional density of mercury (13595.1 kg/m3, irrespective of temperature)
under a standard gravitational field
(9.80665 N/kg or m/s2).
1 mmHg =
(0.001 m) (13595.1 kg/m3 ) (9.80665 N/kg)
= 133.322387415 Pa
On the other hand,
760 Torr is equal to one atmosphere of 101325 Pa.
1 Torr = 101325 Pa / 760 =
133.322368421052631578947 Pa
At Casio's modest level of precision, 1 Torr = 1 mmHg = 133.3224 Pa.
However, that approximation isn't the correct definition of the mmHg.
(2015-11-19 update) The fx-991EX model introduced in 2015 is ten times
more accurate than the fx-991ES class of calculators discussed above.
However, the above rounded
conversion factors were not revised at all, which makes them totally unacceptable at the new precision!
