Saturday, May 11, 2019

Casio Calculators and the Percent Key

Casio Calculators and the Percent Key

Introduction

The percent function on Casio calculators varies based on the calculator itself.  Let's compare six key algorithms on six Casio calculators, five current and one from the past.  We will go from the most consistent behavior to the least.

The calculators used in this study are:

SL-300VC  (four function calculator)
fx-260 Solar II  (scientific calculator - one line display)
fx-300MS 2nd Edition (scientific calculator - one line display)
fx-115ES Plus  (scientific calculator - textbook display)
fx-991EX Classwiz (scientific calculator - textbook display)
fx-115D  (scientific calculator introduced in 1991 - one line display)

Let A and B be real numbers.  In the following examples, required press of the [SHIFT] key are implied as required. 

Algorithm 1:  Multiply

Keystrokes:  A [ × ] B [ % ]

Let A = 82, B = 30

SL-300VC:  24.6 
fx-260 Solar II:  24.6
fx-300MS 2nd Edition:  24.6
fx-115ES Plus**:  123/5 ([ S<>D] 24.6) 
fx-991EX Classwiz**:  123/5  ( [ S<>D] 24.6)
fx-115D:  24.6

A [ × ] B  [ % ] calculates A * B/100.  No surprise that the results will be consistent across the board. 

**Pressing equals ( [ = ] ) is required to complete calculations involving percent calculations for the calculators with textbook display. 

Algorithm 2:  Division

Keystrokes:  A [ ÷ ] B [ % ]

Let A = 82, B = 30

SL-300VC:  273.33333 
fx-260 Solar II:  273.3333333
fx-300MS 2nd Edition:  273.3333333
fx-115ES Plus:  820/3 ([S <> D] 273.3333333) 
fx-991EX Classwiz:  820/3 ([S <> D] 273.3333333)
fx-115D: 273.3333333

A [ ÷ ] B calculates A  * 100/B.   Results are consistent across the board.

Algorithm 3:  Adding Percents

Keystrokes:  A [ × ] B [ % ] [ + ]  

A = 57, B = 11

SL-300VC: 63.27 
fx-260 Solar II: 63.27
fx-300MS 2nd Edition:  63.27
fx-115D:  63.27 

This calculates A * (1 + B/100)

If you tried the exact algorithm with the textbook style calculators like the fx-115ES Plus and the fx-991EX Classwiz, you get an error.  Use the following instead:   A [ (  ] 1 [ +  ] B [ % ] [  ) ] [ = ]

Algorithm 4:  Subtracting Percents

Keystrokes:  A [ - ] B [ % ] [ + ] 

A = 57, B = 11

SL-300VC: 50.73
fx-260 Solar II: 50.73
fx-300MS 2nd Edition:  50.73
fx-115D:  50.73 

This calculates A * (1 - B/100)

If you tried the exact algorithm with the textbook style calculators like the fx-115ES Plus and the fx-991EX Classwiz, you get an error.  Use the following keystroke algorithm instead:   A [ (  ] 1 [ -  ] B [ % ] [  ) ] [ = ]

Algorithm 5:  A - B%

Keystrokes:  A [ - ] B [ % ]

SL-300VC: 12.5 
fx-260 Solar II: 12.5
fx-300MS 2nd Edition: 12.5
fx-115ES Plus:  1784/25 ( [S<>D] 71.36) 
fx-991EX Classwiz:  1784/25 ( [S<>D] 71.36) 
fx-115D: 12.5

We see some difference on how this algorithm is calculated and it depends on the type of calculator used.

For four-function basic calculators and one-line scientific calculators, A - B% calculates the percent change:  (A - B)/B * 100

For the  textbook display calculators, the B is merely divided by 100 and subtracted from A:  A - B/100

Algorithm 6:  A + B%

Keystrokes:  A [ + ] B [ % ]

SL-300VC: 200
fx-260 Solar II: 300
fx-300MS 2nd Edition: 300
fx-115ES Plus:  201/2 ( [S<>D] 100.5) 
fx-991EX Classwiz:  201/2 ( [S<>D] 100.5) 
fx-115D: 300

This is the most inconsistent.  Quite honestly, I don't recommend this algorithm. 

What I learned:

1.  Check your manual on how to use the percent function ( % ), not matter what calculator you use. 

2.  Calculators with textbook display, the percent function ( % ) merely divides the argument by 100.

3.  This is an sample of six calculators, and as you can see, your mileage may vary. 

Have fun calculating,

Eddie

All original content copyright, © 2011-2019.  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.

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