How to Use Scientific Calculator Functions

ARTHUR G. EGGERS, BSEE, MBA
INSTRUCTOR/PROGRAM DIRECTOR
COMMUNITY COLLEGE OF SOUTHERN NEVADA
USING THE SCIENTIFIC CALCULATOR
USING THE
SCIENTIFIC CALCULATOR

A scientific calculator is an invaluable tool while learning math or science.
Scientific calculators are a tool, to help you solve complex problems.

Before calculators became so inexpensive and available we had to learn to
use tables and slide rules to calculate mathematical expressions containing
exponents and logarithms.
BEFORE THE
The scientific calculator, like the slide rule, requires some training to use it
properly and understand the results.

Without the proper understanding of applying the operating principles,
there is no guarantee the answer is correct.
The calculator only performs the functions you instruct it.
In the order you instruct it.

Care should be taken in selecting the scientific
calculator to fit your needs.
The market is flooded with choices.
Most share the same functionality;
the only difference is in the
presentation.
Prices are very reasonable with the less expensive ones starting out around
$20.00.
You may find them cheaper on sale or on-line.

The more complex graphing scientific calculators are available
and very powerful if you plan to study mathematics and
electronics at the engineering level.
They are fun toys if you have nothing
better to spend your money on.
The graphing capability helps you to see
and understand functions.
GRAPHING CALCULATOR
When you enter the equation of a line,
y = mx + b,
The calculator will plot the corresponding line.

Graphing calculators are not required for this course.
If you’ve never used a scientific calculator,
the basic version will be intimidating enough.
GRAPHING CALCULATOR
You will have all the capability you will need
in a less expensive and less complicated basic
scientific calculator.

CALCULATOR FUNCTIONS
The calculator you choose must have more than the basic functions.
You will be performing operations beyond addition, subtraction,
multiplication and division.
This calculator is not a scientific calculator
and is not suitable.
You limited to the basic arithmetic
functions, square root, and percentage.

CALCULATOR FUNCTIONS
This calculator lacks the required functions needed to calculate
scientific expressions.
It can only perform the BASIC functions.
It’s great for balancing your checkbook!

You will need to have a scientific calculator with the following functions:
Degree and radian mode.
Trigonometric functions
Exponential function
FUNCTIONS
Inverse
Trigonometric functions

You will need to have a scientific calculator with the following functions:
Pi [  ].
Inverse function
Square and
Square Root
FUNCTIONS
Change Sign

You will need to have a scientific calculator with exponential
and trigonometric functions, degree and radian mode.
FUNCTIONS
There are several manufacturers to choose from, each is laid out a
little differently, but usually having the same functions available
from the keypad.

It’s important to keep your owners manual or operators guide
handy while you are becoming familiar with the functions
available on your scientific calculator.
THE OWNER’S GUIDE

FUNCTIONS
Aside from the basic functions of addition, subtraction,
multiplication and division…
Many scientific calculators have over a hundred functions available.
Many of the functions require multiple
keystrokes and secondary or tertiary key
modes.

FUNCTIONS
Many of the functions are only available when the correct
MODE KEY is selected.
The function keys are usually blue or yellow keys marked
[ 2nd ] and [ 3rd ].
The key location and labeling
will vary from manufacturer to
manufacturer.
You will have to refer to your
owners guide.

FUNCTIONS
Some scientific calculators have a SCROLL
or UP/DOWN LEFT/RIGHT set of keys to
add functionality.
You must rely on the operators guide to
learn to use these special function
keys!

FUNCTIONS
The most common scientific calculators use
algebraic parenthetical notation.
With algebraic parenthetical
notation, the rules of algebra
are followed when entering
the values correctly.

FUNCTIONS
The Sharp calculator utilizes a proprietary architecture they call
Advanced Direct Algebraic Logic (D.A.L.)
D.A.L. allows the user to enter the
elements of an equation into the
calculator in the exact order they appear
in the expression or from a text.

Reverse Polish Notation
Some scientific calculators, like the HP, use reverse polish notation
(RPN).
RPN is a powerful stacking protocol
where the values are entered first and
them the proper function is applied.
The values move up and down the stack
as the elements are operated on.
HP33S/RPN ($40 -$50)
PROGRAMMABLE SCIENTIFIC CALCULATOR

Reverse Polish Notation was developed in 1920 by Jan Lukasiewicz as a
way to write a mathematical expression without using parentheses and
brackets.
Hewlett-Packard Co., realizing
that Lukasiewicz's method was
superior to standard algebraic
expressions when using
calculators and computers,
adapted RPN for its first hand-
held scientific calculator, the
HP35, in 1972.
HP35 RPN
Programmable Scientific Calculator
LED Display

HP41CV/RPN (Original price 1982: $200.00)
PROGRAMMABLE SCIENTIFIC CALCULATOR

RPN calculators do not have an EQUAL [ = ] key,
but instead have an [ENTER] key.
The ENTER key stores the value or completes
the function.
RPN takes some getting used to if you’ve
never used it.
Once you learn it, problem entry and
solving is a lot quicker.
Two line, alpha/numeric display.

Why Use RPN?
•RPN saves time and keystrokes. You never have to account
for the parentheses while doing calculations. The process is
similar to the way you learned math on paper.
•You can see the intermediary results as you perform your
computations rather than just the answer at the end. This is an
extremely helpful byproduct. Math teachers are using this
feature to improve student understanding of mathematics
•An intermediate result allows the user to check the results and
correct errors more easily. It's easier to follow the stream of
calculation. The user defines the priority of operators.
•RPN is logical because the user first gives the number and
then tells what to do with it.

Exponential Notation
The exponential function will vary between scientific calculators.
Some have an [ENG] key.
The exponential key allows
you to enter values that have a
power of ten associated with
them.
The exponent

Others have an [EE] key.

Others have an [EE] [ 2nd ] key.
The 2nd function key must be
pressed first to access the [ EE ]
key

Others have an [EXP] key.
If neither key is available on your
keypad, you will have to refer to your
owner’s guide to determine how to
invoke the exponential function.

Raising to A Power
The exponential function is not to be confused with the exponent
function of raising a value to a power.
The most common is of course the square key, [ x2 ].
When you enter a value and
press the [ x2 ] key you
calculate the square of the
value.
Like the square key, [ x2 ], a
key marked [ xy ] allows you
to calculate values raised to a
power above 2.
Recall that x-y =
1
y
x

Fractional Exponents
Exponents can be expressed as fractions.
Your scientific calculator will allow you
to enter a value raised to a power that is
expressed as a fraction or a quotient.
When you enter a value “a”, you can
raise it to the power “b/c”, by using the
[ab/c] key.

The Root
The square root key , calculates the square root of a value.
x
You must enter
the value first,
then press the
key.
The same applies for
the key, where
now you are
calculating a root for
any number other
than 2.
x
x y
Recall that x½ = x

Inverse Function
The inverse function is also handy when calculating fractional
values or quotients.
It’s particularly valuable moving
summed values out of the denominator
and into the numerator.
NOTE TO ET STUDENTS:
You will recognize the value when you
learn to analyze parallel circuits.
The inverse key may be a
[1/x ] key.
Pressing this key results in
giving you the reciprocal
value.

Inverse Function
The inverse function is also handy when calculating fractional
values or quotients.
NOTE TO ET STUDENTS:
You will recognize the value when you
learn to analyze parallel circuits.
The inverse key may also be a
[ x-1 ] key.
Recall x-1 = 1/x

On-board Functions
The display of your calculator only shows
the first ten or so digits.
There are more digits stored in memory
beyond what you see in the display.
With values like , the non-repeating,
infinite values not shown are stored in
memory to the limits of your calculator’s
storage and display capability.
To properly use the power of the calculator, it’s important to use on-
board function keys like the [  ] key, and not merely enter the truncated
value 3.14 when  is required in a computation.
The reason for this is,  is a non-repeating,
infinite number that is best treated by the
calculator.

On-board Functions
When you take the sine, cosine, or tangent
of a number, the display only shows you
part of the result.
Other on-board functions like sine [ sin ], cosine [cos ], and
tangent [ tan ] are available from the keypad and must be used to
the maximum capability of the calculators storage and display.
For example:
To calculate the sin30, you first enter
30, then press the [ sin ] key to get 0.5.
It’s important to note that you must enter
the value first, then press the
trigonometric function key to calculate
the function.

On-board Functions
When you take the inverse sine, inverse
cosine, or inverse tangent of a number,
again the display only shows you part of
the result.
Other on-board functions like inverse sine [ sin-1 ], inverse cosine
[cos-1 ], and inverse tangent [ tan-1 ] are also available from the
keypad and must be used to the maximum capability of the
calculators storage and display.
For example:
To calculate the tan-11.33, you first enter 1.33,
then press the [ tan-1 ] key to get 53.1°.
It’s important to note that you must enter
the value first, then press the
trigonometric function key to calculate
the function.
These functions also require that you
first press the [2nd] key.

Memory
Memory in a scientific calculator is a nice option, but not a necessity.
Many come equipped with a memory
storage location on-board and available on
the keypad.
The [ STO ] and [ RCL ] keys are the keys
for storing one element at a time in
memory.

Memory
Some scientific calculators use an [M+]
and [M-] as well, to operate on elements
stored in memory.
This function is handy if you are adding
or subtracting from the value stored in
memory.

Memory
Some scientific calculators allow you to
swap values in a memory location by
using the [ xy] key.
For this calculator you would use the
[2nd] key and press the [] key to
perform the swap.

Programmable Scientific Calculators
Programmable scientific calculators, like memory are nice to have,
but not a necessity.
Programmable scientific calculators are
very powerful, normally used by scientists
and engineers, but beyond the
requirements for this course.
You will have your work cut out for you if
you decide to purchase a programmable
scientific calculator.
You will have wasted your money if you
don’t learn to use its full capability.

Programmable Scientific Calculators
Programmable scientific calculators, like memory are nice to have,
but not a necessity.
Programmable scientific calculators are very powerful, normally
used by scientist and engineers, but beyond the requirements for
this course.
Programmable calculators become
powerful when the problems you are
solving become repetitive or iterative.
Again, a fun toy, but not required.

Planning your Entry
With all of this in mind, it’s important to plan how you enter the
values in you calculator.
You have to obey the rules of mathematics.
Remember all those laws: associative, distributive, commutative…
I usually start with values in the denominator, especially if there are
values that have exponentials.
For example:
1
2
C
X
fC


If f = 500Hz and C = 0.01F
  
6
1 1
2 2 500 0.01 10
C
X
fC Hz F
  
 


Planning your Entry
I would approach the problem by first entering the exponential in the
denominator 0.001X10-6F
Enter 0.01 and press [ EE ] or [ ENG ], the calculator will prompt you for the
exponent,
Enter 6 and press [  ] key to change the sign of the exponent.
Press [  ] key to multiply, and enter 500.
Press [  ] key to multiply, and enter [  ].
Press [  ] key to multiply, and enter 2.
Press [  ] key to multiply, and then press the [ 1/x ] or [ x-1 ] key to invert the
value in the denominator.
The value is now in the numerator, multiplied by the understood value of 1
You’re done!
You should have 31.8X103 or 31831.

The Power of Your Scientific Calculator
Your scientific calculator has many other functions that are available.
•Hyperpolic Functions
•Logarithmic Functions
•Inverse Logarithms
•The Natural Logarithm
•Fractional Exponents
•Summation
•Statistical Functions
•Standard Deviation
•Averaging (Statistical Mean)
•Scientific Notation
•Engineering Notation

CALCULATOR SKILLS
You can only become skilled using your calculator if you take the time to
learn how to properly use it.
Keep your owners guide handy and with you.
Work sample problems so that you gain proficiency.
Practice using your calculator!

How to Use Scientific Calculator Functions

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