Sunday, February 26, 2023

TI-84 Plus CE Wish List and YouTube Shorts

TI-84 Plus CE Wish List and YouTube Shorts



TI-84 Plus CE Wish List



Disclaimer:  I do not work for Texas Instruments nor do I know when (or if) TI is working on and publishing operating version 5.9, 6.0, etc.  This is my opinion only (the opinion of a math and calculator enthusiast).


This focuses on the United States version of the TI-84 Plus CE series.


I would like to see the following in the next update:


1.  Simplification of radicals and square roots.*   Currently the series only has decimal approximations.


Examples:

√440 returns  2 * √110

√75 + √125 returns 5 √5 + 5 √3


2.  Mathematical operations returning exact results in terms of π.*  Like #1, the series only has decimal approximations.


Examples:

In radians mode,  cos^-1 (1/2) returns π/3

2 π - 3/8 * π  returns 13/8 * π


3.  Base mode and conversions.  With the exception of the classic TI-85 and TI-86, the TI-80s do not have a base mode nor base conversions.  I would like to see that added, make room under the test menu.    


4.  More colors than 15 please.   Maybe an RGB (red-green-blue) function in the TI-BASIC programming language?  


With Gratitude to TI. 


YouTube Short:  https://youtube.com/shorts/KOQs95qCHtg?feature=share



* FYI:  #1 and #2 are available on the TI-83 CE Premium from France.  



YouTube Shorts



From time to time, I will post YouTube short videos (60 seconds or less) to my YouTube channel (which has been a long time starving for content):


https://www.youtube.com/@theedspage


My channel covers primarily math and calculators.  



Eddie



All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Saturday, February 25, 2023

HP 12C: The C Indicator - Odd Period (Calculating Payment)

HP 12C: The C Indicator - Odd Period (Calculating Payment)



There is a C indicator on my HP 12C!





When I bought a HP 12C calculator that was manufactured in Brazil, there was a C indicator on it.  It was an odd-period calculation switch that has been a documented feature of the HP 12C.  



Odd Period of an Annuity 



An odd period of any annuity occurs when the present value (example:  loan proceeds) is received before the first period (example: month) occurs. 


On the diagram below:


PV:  proceeds received


PV0:  balance at the start of the first period.   This the proceeds plus any interest accrued during the odd period.  In general, PV0 > PV.  



For example:  loan proceeds of $10,000 is received on March 26, 2022 (the PV),  with the first payment due at the end of the next month, April 30, 2022.  In this case, the loan proceeds were received five days before the "official" first month of the loan which starts on April 1, 2022. The odd period is 5 days, or 5/30 of a month.


In general, all months are considered to be 30 days under a 30/360 calendar system.   You can use the actual calendar (365/366-day year) if you wish.  


To account for an odd period, add the fractional part of the odd period to the number of payments and store it the [ n ] variable.   


There are two ways to calculate odd period interest:  simple interest and compound interest.



HP 12 Settings for Odd Period Interest



C indicator:   the odd period interest is calculated using compound interest


No C indicator:  the odd period interest is calculated using simple interest


The setting is set by pressing [ STO ]  [ EEX ].



Casio FC-200V Settings for Odd Period Interest


The Casio FC-200V (and FC-100V (1st and 2nd editions)) has a setting for odd periods.  In the Compound Interest app (CPMD), press [ SETUP ] and select dn, then select between CI and SI.  


CI:   the odd period interest is calculated using compound interest


SI:  the odd period interest is calculated using simple interest


This set up is also present in the Simple Interest app (SMPL).



Formulas


If your calculator doesn't have odd period settings, you will need to calculate PV0.  Once PV0 is calculated, then proceed to calculate payment, ignoring the odd value for n.  


Compound Interest:


PV0 = PV × (1 + I%÷(n×100))^(odd period)


Compound Interest - Monthly Payment, 30/360 Day Calendar:


PV0 = PV × (1 + I%÷(1200))^(days ÷ 30)


Simple Interest:


PV0 = PV × (1 + I% ÷ 100 × odd period)


Compound Interest - Monthly Payment, 30/360 Day Calendar:


PV0 = PV × (1 + I% × days ÷ 36000)


where:

PV = proceeds

PV0 = balance at the beginning of the first period

I% = annual interest rate (not converted to decimal)

odd period = fraction of the year which the odd period represents

days = days of the odd period


These formulas assume end-of-period payments, but also work equally as well for beginning-of-period payments.   In practice the difference between the two methods result in a small difference.



Example


Facts:

* Loan proceeds:  $17,755.00

* Interest rate: 7%

* Number of monthly payments: 60, payments are due at the end of the month

* Odd period:  15 days, 30/360 calendar


Find the payment.



Compound Interest


HP 12C:  press [ STO ] [ EEX ] until the C indicator is on

[ f ] [ x<>y ] (CLEAR FIN)

[ g ] (END)

60.5 [ n ]

7 [ g ] (12÷)

17755 [ PV ]

[ PMT ] returns -352.59


Casio FC-200V:  set dn to CI

[ CMPD ]

Set: End

N = 60.5

I% = 7

PV = 17755

P/Y = 12, C/Y = 12 

Solve PMT for -352.59


Others:

PV0 = 17755 × (1 + 7 × 15 ÷ 36000)= 17806.71

N = 60

I%/YR = 7

PV = 17806.79

P/Y = 12, C/Y = 12

Solve PMT for -352.59



Simple Interest


HP 12C:  press [ STO ] [ EEX ] until the C indicator is off

[ f ] [ x<>y ] (CLEAR FIN)

[ g ] (END)

60.5 [ n ]

7 [ g ] (12÷)

17755 [ PV ]

[ PMT ] returns -352.60


Casio FC-200V:  set dn to SI

[ CMPD ]

Set: End

N = 60.5

I% = 7

PV = 17755

P/Y = 12, C/Y = 12 

Solve PMT for -352.60


Others:

PV0 = 17755 × (1 + 7÷1200)^(15 ÷ 30) = 17806.79

N = 60

I%/YR = 7

PV = 17806.71

P/Y = 12, C/Y = 12

Solve PMT for -352.60


As you can see, little, if any difference between the two methods.




Are there are any other calculators that can handle odd-period calculations?


I'm hesitant to say yes.  How do we know if a finance calculator or the finance mode of a scientific or graphing calculator has handles odd-period calculations?   Check the set up or mode settings.  If you see an option to set odd periods to simple interest or compound interest, then yes.   If not, use the formulas stated above to first calculate PV0 and proceed.  


For the record, neither  the Texas Instruments BA II Plus nor the Sharp EL-738F do not have not odd-period calculation settings.  No graphing calculator or scientific calculator with time value of money modules has this that I know of.  


On the Calculated Industries Qualifier Plus IIIFX, use the PV0 amount for the Loan Amount.   This calculator can find the prepaid interest, which is based on 30/360 day year, simple interest.  



Sources


HP 12C Financial Calculator User's Guide.  Hewlett Packard.  Edition 5.  San Diego, California, United States.  2008.  pp. 50-53


FC-200V, FC-100V (2nd Edition/Financial Consultant User's Guide.   Casio.  Shibuya-ku, Tokyo, Japan.  2021




I will back to the Saturday-Sunday schedule starting on March 4, 2023.  


Eddie


All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Saturday, February 18, 2023

Numworks Software Version 20 Now Available

 Numworks Software Version 20 Now Available 


Click here for details:

https://www.numworks.com/calculator/update/version-20/


Highlights:

*  Separate Finance and Distribution Applications

*  Pressing the divide key [ ÷ ] prior to number entry cycles between:  Ans divided by denominator, fraction, mixed fraction.  

*  Pressing the Home Key then the 0 key gets the shortcut to Settings

*  The new Elements app is available.  We can display each element by its family, s/p/d/f blocks, type of metals, molar mass, electronegativity, melting temperature, boiling temperature, and atomic radius.  Each attribute is shown separately.

* When a value is highlighted in any app, except in Python, pressing [ shift ] (sto→) will give you a prompt to store the amount in a variable.  As a reminder, variables can have more than one character.

*  In the Grapher app, points of interest (zeroes/roots, minima, maxima, points of inflection, etc.) will have black dots.

*  Also in the Grapher app, the ability to find integrals is added to the toolbox.

*  Inverse trig functions are now labeled as arcsin, arccos, and arctan.  

*  Degree and degree minute second templates are loaded from the Toolbox > Units and constants > Length and angle > Angle submenu.

* Additional information is added to angle, trigonometric, and vector calculations.  

* We can add and subtract percents directly.   


There seems to not be additions to the Python programming module (yet).


To update:  just sign in to your Numworks account.  Then connect your calculator, select Update under the Calculator and follow the prompts.  Easy as that!


Thank you, Numworks! 


Eddie



HP Prime: Interval Arithmetic

HP Prime:  Interval Arithmetic



Interval Arithmetic



In computing, we are working with approximate calculation.  Often a number can be stated as a small interval to account for round off error.  


An interval is a range of two numbers from a to b:  [a, b].  The variable a represents the lower bound, with the variable b represents the upper bound.  There is no restriction on how large or small the interval is.


For example, the interval [ 81.8, 82.2 ] represents the range from 81.8 to 82.2.  This could stand for a calculated value of 82.0 with a plus-or-minus error of 0.2.  


Applying a general function of one function, f(x) to interval, results in this:

f([a, b]) = [ min(f(a), f(b)), max(f(a), f(b)) ]


Applying this to the square root function to intervals:

√([a,b]) = [ min(√a, √b), max(√a, √b) ]


The arithmetic functions for intervals are defined as:


[a, b] + [c, d] = [a + c, b + d]

[a, b] - [c, d] = [a - d, b - c]

[a, b] × [c, d] = [min(a × c, a × d, b × c, b × d), max(a × c, a × d, b × c, b × d)]

[a, b] ÷ [c, d] = [min(a/c, a/d, b/c, b/d), max(a/c, a/d, b/c, b/d)]


Scalar multiplication, given the scalar is positive:


s × [a, b] = [ s × a, s × b ]



HP Prime Interval Programs



INTERVALHELP:  help screen for interval arithmetic functions

INTERVALADD:  adding two intervals

INTERVALSUB:  subtracting two intervals

INTERVALMUL:  multiply two intervals

INTERVALDIV:  divide two intervals


In the Home mode, use the curly brackets (used for lists { }), to type the intervals.  For example, the interval [ 81.8, 82.2 ] would be typed {81.8,82.2}.


EXPORT INTERVALHELP()

BEGIN

// 2022-12-22 EWS

PRINT();

PRINT("Interval Arithmetic");

PRINT("Use curly brackets {}");

PRINT("");

PRINT("INTERVALADD({a,b},{c,d})");

PRINT("add intervals");

PRINT("");

PRINT("INTERVALSUB({a,b},{c,d}");

PRINT("subtract intervals");

PRINT("");

PRINT("INTERVALMUL({a,b},{c,d})");

PRINT("multiply intervals");

PRINT("");

PRINT("INTERVALDIV({a,b},{c,d})");

PRINT("divide intervals");

END;


EXPORT INTERVALADD(v1,v2)

BEGIN

RETURN v1+v2;

END;


EXPORT INTERVALSUB(v1,v2)

BEGIN

RETURN v1-REVERSE(v2);

END;


EXPORT INTERVALMUL(v1,v2)

BEGIN

LOCAL v3;

v3:=CONCAT(v1*v2,v1*REVERSE(v2));

RETURN {MIN(v3),MAX(v3)};

END;


EXPORT INTERVALDIV(v1,v2)

BEGIN

INTERVALMUL(v1,1/REVERSE(v2));

END;


Download a zip file here:  https://drive.google.com/file/d/1L8mmnm3xx58PVjavDROCiZAafBOCsH9o/view?usp=share_link



Example



Interval 1 = {13, 29}

Interval 2 = {10, 14}


Add:  {23, 43}

Subtract:  {-1, 19}

Multiply:  {130, 406}

Divide:  {0.928571428572, 2.9}



Source


Moore, Ramon E.  Mathematical Elements of Scientific Computing  Holt, Rinehart, and Winston, Inc: New York.  1975.  ISBN 0-03-088125-0




Until next time and wish you all well,


Eddie  


All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Saturday, February 11, 2023

Sum and Product Problem with the Casio fx-4000P

Sum and Product Problem with the Casio fx-4000P



The Sum and Product Problem


For the numbers a and b with the sum s, and product p:


a + b = s

a * b = p


Let's find a solution for a and b:


a + b = s

b = s - a


a * b = p

a * (s - a) = p

a * s - a^2 = p

0 = a^2 - a * s + p


a = (s ± √(s^2 - 4 * p))/2


Then:


b = s - a

= s -  (s ± √(s^2 - 4 * p))/2

= (2*s)/2 -  (s ± √(s^2 - 4 * p))/2

= (2*s -s ±√(s^2 - 4 * p))/2

=  (s ± √(s^2 - 4 * p))/2


Note that addition and multiplication are communitive.  


Without loss of generality, let:


a = (s + √(s^2 - 4 * p))/2


b = (s - √(s^2 - 4 * p))/2


Verification:


a + b 

= (s + √(s^2 - 4*p))/2 + (s - √(s^2 - 4*p))/2

= (s + √(s^2 - 4*p) + s - √(s^2 - 4*p))/2

= (2 * s)/2

= s


a * b

= (s + √(s^2 - 4 * p))/2 * (s + √(s^2 - 4 * p))/2

= (s/2)^2 - (√(s^2 - 4 * p)/2)^2

= s^2/4 - (s^2 - 4 *p)/4 

= (s^2 - s^2 + 4 * p)/4

= (4 * p)/4

= p



Casio fx-4000P Program:  Sum and Product Problem


This program can be adopted to many programming and graphing calculators. 


Program:


"A+B=":?→S:

"AB=":?→P:

(S+√(S²-4P))÷2→A◢

S-A→B



Examples


S:  Sum

P:  Product


Example 1:

S = 12, P =32;

Results: 8, 4


Example 2:

S = 8, P = 15;

Results: 5, 3



Enjoy!  Until next time,


Eddie


All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

 

Wednesday, February 8, 2023

Review: NY-991MS Ewriter Calculator Review

 Review: NY-991MS Ewriter Calculator Review (LINGSFIRE)







Quick Facts


Model: NY-991MS

Company: NewYes/LINGSFIRE

Price:  About $18 - $25 (purchased on Amazon)

Power:  Solar with battery (CR2032)

Display:  Two lines, numerical and fractions.  Numbers can have up to 10 digits. 



Calculator with an Electronic Writing Board


The NY-991MS is one of a new breed of calculators to come with a mini electronic writing board attached.   For this calculator, the pen is stored in a lower left-hand corner compartment.   There is a lock switch at the top of the calculator.  If the lock switch is on the left position, the board is unlocked, therefore the board to be erased with the press of a clear button.  If the lock switch is on the right, the board is locked and nothing can be erased.   


It is the writing board that got me interested in buying this calculator and is a neat feature to write quick notes.  So far, the NY-991MS is the most advanced calculator that has this feature.  


Other models include (not an all inclusive list):


JEOEUS JEOEUS-005:  basic four function calculator


LINGSFIRE:  similar to a Casio fx-300 MS


Laelr:  similar to a low-cost scientific calculator Sharp EL-501XBGR


On my calculator, the pen was hard to get out (but locks in nicely), so I keep a pen in a separate bag near this calculator.   


I love the hard folding case that the NY-991 MS comes in.  Not only it looks professional, the case is hard and protects both the calculator and the writing tablet.  I also love how large the numbers and functions are on the screen.



Not Quite A Casio fx-115MS


Now let's talk about the functionality.  I would place the NY-991 MS somewhere between the Casio fx-300MS and the Casio fx-115MS.   


Let's get the ugly out of the way.  The manual is terrible.   The manual has examples of functions that are not even present, mislabels keys, and has a lot of spelling errors.   If this is someone's first calculator, then the person is going to have a rough experience if they tried to follow the manual.   Put in some effort and proofread, NewYes.  


The NY-991MS has four main modes:


0:  COUNT.   This is the regular operating mode of the calculator. 

1:  STAT:  One-variable statistics

2:  REG:  Regression

3:  CMPLX:  Complex Number arithmetic



COUNT MODE


While a lot of functions are self-explanatory, some need to be pointed out due to some idiosyncrasies.  


The angle setting is a toggle button:


[ D|R ]: switch between degrees and radians.  There is a "G" indicator too, but the NY-991MS does not have a gradian mode.


[ 2ndF ] (D←→R):  switches between degrees and radians, plus converts the angle in the display.


When the calculator is in degrees mode, there is a "TY" indicator on the screen.  I have no idea what TY stands for nor does the manual explain this indicator.  



The number format has a three-way toggle button:


[ F/S ] (number):  Fixed mode

[ F/S ] [ F/S ] (number):  Scientific mode

[ F/S ] [ F/S ] [ F/S ]:  Float mode



The [ DMS ] key is dual purpose:  entering degree, minute, or second markers during calculations.  After the equals key is pressed, the key switches the number between degrees-minutes-seconds and decimal degrees format.   


The key sequence [ 2ndF ] ( ←→DEG) does not do anything.



The logarithm keys operate differently from most scientific calculators:


[ log ]:  takes the logarithm of any base.  The syntax:  log(number,base)

[ lg ]:  common logarithm

[ ln ] : natural logarithm



The polar/rectangular conversions do not accept parenthesis or a syntax error occurs.


OK:

5,3 [ →rθ ] returns  r (stored in X) returns = 5.830951895 and θ (stored in Y) returns 30.96375653


(5,3) [ →rθ ] gives an error


Similar with the →xy function.    I thought this key was broken or useless until I figured it out by accident.  The manual does not show the correct way to use the polar/rectangular conversion.



The key [ A^m_n ] is the permutation key.  No idea why this is labeled A.   The more appropriately labeled C^m_n is the combination key.



We can store expressions for later evaluation.   Press [ 2ndF ] (LRN) to store the expression.  Press [ COMP ] to evaluate it.  You will be prompted for the variables.  The stored expression is erased when the calculator is turned off.  There is no solve feature.  



Calculus functions:


Derivative:  d/dx( function of X, value)

Definite Integral:  ∫( function of X, lower limit, upper limit)



There is this weird arrangement of variables.  A, B, C, D are in one line while X, Y, and Z are on the 2nd row.  In this mode we have a bug:  whenever a value is stored in A, the display returns 0.   The value is retained in A though.



Want to enter numbers in scientific notation?  Press [ 2ndF ] ( Exp ) to get the E.



STAT


One variable stats are entered using the [ DATA ] button.  What I like about the statistics mode is that parameters are on the keyboard, that can be accessed by the [ ALPHA ] key.   However, s_x does NOT return the sample deviation, but the population deviation.  Likewise, (s_x)^2 returns the population variance.  


Population Deviation



REG


There are six regressions, which the variables are mislabeled in the manual.  Here are the true regression equations used:


1.  Lin:  Linear Regression,  y = a*x + b

2.  Quad:  Quadratic Regression, y = a*x^2 + b*x + c

3.  Inv:  Inverse Regression, y = a/x + b

4.  Pwr:  Power Regression, y = b * x^a

5.  Exp:  Exponential Regression, y = b * e^(a*x)

6.  Log:  Logarithmic Regression, y = a*ln x + b


In essence, other than quadratic regression, the variable a is the slope and the variable b is the y-intercept. 


The [ ALPHA ] key is needed to use the prediction functions x-hat and y-hat.  



CMPLX


The complex number mode is, as expected, limited.  Allowable operations are the arithmetic functions, the reciprocal, and the square functions.  Enter the imaginary part with the [ i ] button.    


Results are shown on part at a time between the real and imaginary part.   Press [ 2ndF ] [ i ] (←.→) to switch between the real and imaginary parts.  There is another key that is exclusive to this mode:


[ |R| ]: absolute value.   This operates only after the calculation is completed by pressing the equals key.  


[ 2ndF ] (ARG):  argument.  Likewise, this operates only after the calculation is completed by pressing the equals key.


The manual mentions a conjugate function, which isn't present on the calculator.  


Final Thoughts


This calculator had potential and unfortunately, with the arrangement of keys, mislabeling of the deviation and variance, the unusual syntax of some functions, and the horrible manual, I cannot recommend this calculator unless you are an expert user.   I was able to figure out the functions due to the fact I had a Casio calculator to compare results.   The electronic board and the beautiful folding case, while very nice, may not be enough to make up for the faults for some.  Not recommended for a beginner at all, especially if the user has to depend on the manual to use it.  



Eddie 




All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Saturday, February 4, 2023

RCL 40 Book On Sale

RCL 40 Book On Sale



The fantastic book, RCL 40: Recollection, Reinvention, & HP Calculators, edited by W.A.C. Mier-Jedrezejowic, Ph. D, Mark Power, and Bruce Horrocks is a collection of articles from mathematicians, programmers, and calculator enthusiasts.  This books covers the legendary HP 41C, the Swiss Micros equivalent, the DM41 family, to engineers' experiences working for Hewlett Packard.   I wrote a chapter in the book where I talk about my experiences with the HP 41C and DM41X.   

RCL 40 is a celebration of the HP 41C and calculators.   

To order, please click here.  The book is published by the HPCC in the United Kingdom.  

Eddie 



All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


Casio fx-9750GIII: Effects of Rounding

 Casio fx-9750GIII:  Effects of Rounding



How Accurate?


The program ROUNDS compare true results against the true results in one of five calculations:


1.  A × B × C

2.  A × B ÷ C

3.  √(A^2 + B^2 - C^2)

4.  A ÷ B ÷ C

5.  (A + 1 ÷ B)^C


The rounded result is calculated after rounding after each step.


For example:  A × B × C


True result:  

T = A × B × C


Rounded Result:

R = round(A × B)

R = round(R × C)


The absolute error percentage is calculated.   



Casio fx-9750GIII Program:  ROUNDS


"2022-11-23 EWS"

"EFFECTS OF ROUNDING"

"# OF PLACES"?→N

"A"?→A

"B"?→B

"C"?→C

Menu "SELECT OPERATION",

"A×B×C",A

"A×B÷C",B

"√(A^2 + B^2 - C^2)",C

"A÷B÷C",D

"(A+1÷B)^C",E

Lbl A

RndFix(A×B,N)→R

RndFix(R×C,N)→R

A×B×C→T

Goto 1

Lbl B

RndFix(A×B,N)→R

RndFix(R÷C,N)→R

A×B÷C→T

Goto 1

Lbl C

RndFix(A²+B²,N)→R

RndFix(√(R-C²),N)→R

√(A²+B²- C²)→T

Goto 1

Lbl D

RndFix(A÷B,N)→R

RndFix(R÷C,N)→R

A÷B÷C→T

Goto 1

Lbl E

RndFix(A+1÷B,N)→R

RndFix(R^C,N)→R

(A+1÷B)^C→T

Goto 1

Lbl 1

RndFix(100×Abs (R-T)÷T,5)→E

ClrText

Locate 1,3,"ROUNDED:"

Locate 9,3,R

Locate 1,4,"ACTUAL:"

Locate 9,4,T

Locate 1,5,"ERROR%:"

Locate 9,5



Example:


Let A = 13.946, B = 11.9765, C = π^3/4

Round to 2 decimal places (N = 2)


1.  A × B × C

Rounded:  1294.67

Actual:  1294.700174

Error:  2.33*10^-3 %


2.  A × B ÷ C

Rounded: 21.55

Actual:  21.54715585

Error:  0.0132%


3.  √(A^2 + B^2 - C^2)

Rounded: 16.67

Actual:  16.66855254

Error:  8.68*10^-3 %


4.  A ÷ B ÷ C

Rounded: 0.15

Actual: 0.1502208155

Error: 0.14699%


5.  (A + 1 ÷ B)^C

Rounded: 778927217

Actual:  778710708.2

Error:  0.0278%



Enjoy,  


Eddie 


All original content copyright, © 2011-2023.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


TI 30Xa Algorithms: Greatest Common Divisor

TI 30Xa Algorithms: Greatest Common Divisor To find the greatest common divisor between two positive integers U and V: Let U ≥ V. ...