Overview of methods for correctly using a calculator

Different calculators operate in different ways. The order in which numbers, operations, and functions are entered, the markings of the keys that perform functions, the way the information is displayed, and the way the calculator is set to interpret information entered $($e$.$g$.,$ whether angles are in degrees or radians$),$ can all vary widely from calculator to calculator. Therefore, it is highly recommended that you make a habit of using the specific calculator with which you are familiar for all of the work in your physics course.

The order in which information is entered into the calculator and operations are performed matters! This is called $$precedence of operation,$$ and you must familiarize yourself with it$.$ In general, you cannot simply enter an expression into a calculator in the order you read it and obtain the correct result! A very helpful strategy for avoiding precedence of operation errors when evaluating longer expressions with a calculator is to perform intermediate calculations one step at a time:

Select smaller portions of the whole expression.

Use the calculator to perform these intermediate evaluations.

Rewrite the expression using the intermediate results.

Proceed until the entire expression has been evaluated.

Below are calculator keys and operations which you must be able to use correctly for a physics class:

Clear key $($you may need to use different keys to clear the display and clear values from the memory of the calculator$)$

Number keys $(09)$

$,$ including the decimal point $(.)$

Operation keys $(+,,\backslash$times $,-$:$,=)$

Change sign key $($note that on some calculators the change sign key looks very similar to the subtraction key; these two keys do NOT do the same thing so you must be careful to distinguish between them$)$

Square root $()$

$,$ square $($x$2)$

$,$ inverse $(1/$x

or x$1)$

$,$ and exponent $($ xy

or $)$

operations. You may need to use a shift $($or $2$nd$)$ key on the calculator for some of these operations.

Changing the angle units between degrees $($deg$)$

and radians $($rad$)$

$($some calculators display the angle units currently set, others don$$t$,$ although you should be able to change these units in your calculator$$s settings$)$

Trigonometric functions: sine $($sin$)$

$,$ cosine $($cos$)$

$,$ and tangent $($tan$)$

$,$ as well as inverse trigonometric functions: arcsine $($arcsin

$,$ or sin$1)$

$,$ arccosine $($arccos

$,$ or cos$1)$

$,$ and arctangent $($arctan

$,$ or tan$1)$

$.$ You may need to use a shift $($or $2$nd$)$ key for some of these operations. $($Note: make sure you must use the correct setting of angle units for both trigonometric functions and inverse trigonometric functions$)$

Scientific notation: you need to know the key that you use to enter numbers in scientific notation $($e$.$g$.$ E$,$ EE$,$ or EXP$),$ and the way in which your calculator displays numbers that are expressed in scientific notation.

Other keys that may also be useful: parentheses $($which can be used to group terms and reduce precedence of operation errors$),$ constants $($such as $\backslash$pi

$),$ memory to store intermediate results, logarithm $($log$)$

and natural logarithm $($ln$)$

$,$ statistics $($STAT$),$ and more.

Learn your calculator $($example $1)$

Let's evaluate the quantity v$=15$meter$+5$meter$2$second$+3$second

$.$ You can also do this evaluation in your head. That$$s an important strategy for verifying that you are using your calculator correctly! Let$$s apply the one$-$step$-$at$-$a$-$time strategy. First, perform the addition in the numerator using the calculator:

v$=20$meter$2$second$+3$second

$.$

Then, use the calculator to perform the addition in the denominator:

v$=20$meter$5$second

$.$

Finally, use the calculator to perform the division to obtain the correct final numerical answer:

v$=4$meter$/$second

$.$

Note that if you enter the values and operations into your calculator in exactly the same order that you read them in the expression, $15+5-$:$2+3$

$,$ your calculator will display the wrong answer for the expression. This would be a precedence of operation error! An alternative approach in a case like this is to place parentheses around the terms in the numerator and denominator separately in your calculator: $(15+5)-$:$(2+3)$

$.$ When entered this way, your calculator, which follows the order of operations, gives the correct answer. Now try a problem on your own.

Part A $-$ Average acceleration

Use your calculator to evaluate a$=3\mathrm{.}7$meter$/$second$13\mathrm{.}9$meter$/$second$21\mathrm{.}4$second$7\mathrm{.}2$second

$.$

View Available Hint$($s$)$for Part A

Hint $1$for Part A$.$ Change sign vs subtraction key

Hint $2$for Part A$.$ One$-$step$-$at$-$a$-$time

Hint $3$for Part A$.$ Verify proper use of the calculator

$1\mathrm{.}24$meter$/$second$2$

$0\mathrm{.}718$meter$/$second$2$

$11\mathrm{.}5$meter$/$second$2$

$0\mathrm{.}718$meter$/$second$2$