Calculator Fucntion Input and Output if You Dont Know All Values
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Using a scientific calculator
Introduction
The course describes some of the main features of a scientific figurer and encourages you to use your estimator, both for everyday arithmetic and for more complicated calculations that use the function keys as well. Fundamental sequences, which describe which keys to press, are included in all the activities, so you lot tin endeavor out the ideas straightaway.
Due to the wide range of scientific calculators bachelor, for the purposes of this course we will be concentrating on the Casio fx-83ES model. Other calculators may function differently to the methods described inside this class.
This calculator is used on the Open up University courses Starting with maths (Y182) and Discovering mathema t ics (MU123), but would as well exist useful for many other courses requiring the employ of a scientific reckoner.
This OpenLearn course is an adapted extract from the Open University course MU123 Discovering Mathematics.
Learning outcomes
Subsequently studying this course, you should exist able to:
-
sympathize the basic functions on your estimator
-
understand which calculator functions are needed for a given problem
-
understand what may get wrong when entering calculations and know how to fix them
-
employ knowledge of calculator functions to a range of mathematical calculations.
1 Getting to know your computer
The showtime eleven sections describe how to apply the calculator and how to perform unlike types of calculations. Section 12 contains a calculator reference guide that y'all tin refer to as needed for some of the principal key sequences.
This class is not an exhaustive list of all the calculator's features. If y'all are using a different computer, you should use the corresponding features of your own calculator to do the activities in this guide. You may need to refer to your figurer manual to practice this.
Yous may be able to download the transmission for your reckoner from the manufacturer's website.
The first step in using your calculator effectively is to make sure that you are familiar with the layout of the keys on the keypad, and that you tin can understand the information on the display.
Figure 1 shows the different parts of the Casio fx-83ES calculator.
Figure 1 A typical scientific figurer
If you are using a different model of calculator, make sure that you can identify similar functions on your model.
The calculator is switched on using the 
key at the tiptop right-paw corner of the keypad. Effigy two shows the different elements of this calculator's display.
Throughout this section, calculator keys will be indicated using the symbol on the fundamental enclosed in a box, for example .
Figure two The figurer display
The lower half of the keypad contains the number keys, keys for the basic operations of improver, subtraction, division and multiplication, and the 
key, which is pressed when you lot desire the reckoner to display the result of the calculation yous have entered. The keys 
used to insert brackets into a calculation are in the centre of the row in a higher place the number keys.
Many keys on the calculator have more than ane use. The master role of a central is printed in white on the key itself. The second function of the central is printed in yellowish to a higher place the key, and is accessed by pressing the 
button before pressing the key. When yous printing the push button, the symbol ' 
' appears at the acme left-hand corner of the calculator display to remind you that the push button has been pressed. It disappears when you press some other key. Some keys also take a tertiary part, printed above the cardinal in cherry-red. These functions let numerical values stored in the calculator memories to be used within calculations and are accessed by pressing the 
button before the appropriate key. When the button is pressed, the symbol ' 
' is shown at the acme of the reckoner display. You will larn how to apply the calculator memories later in department 4.
The calculator manual describes this 2nd function equally the 'alternate' function of the cardinal.
Some calculator operations are accessed through a system of menus that are displayed on the estimator screen, as shown in Figure 3. The required menu selection is selected past pressing the number central associated with the option, as given on the calculator screen.
Figure 3 A typical calculator on-screen menu
When describing how to apply various calculator functions, this guide gives the verbal keys that you need to press using the symbols shown on the keys. This is known equally a 'fundamental sequence'. If the key sequence accesses the second function of a key, or a role from a carte du jour, the name of this role will be given in brackets at the appropriate indicate in the key sequence. Names in brackets are thus non keys that y'all press but simply describe the function that is accessed using the previous key sequence. For example, to turn off the figurer, printing 
(OFF). In this notation, (OFF) is non a cardinal that y'all printing, but is the name of the second function of the key, which is accessed with the primal.
The calculator has many modes of operation that affect how mathematics is entered and displayed. These will exist described after in this guide, just before progressing any farther you should reset your calculator to the default course settings.
Activity 1 Initialising your calculator
To initialise your computer to the default course settings, turn information technology on and then enter the following two cardinal sequences:
(CLR) 
(Setup) (Yep)
(SETUP) 
(Norm) 
Note that in the first fundamental sequence, 'CLR' (which is brusk for 'articulate') is the second role of the key, and 'Setup' is the name of the on-screen menu choice respective to the key. 'Yep' is the name of the on-screen carte option corresponding to the key. This key sequence clears all previous 'setup' settings on the calculator.
In the second cardinal sequence, 'SETUP' is the name of the 2nd function of the key, and 'Norm' (brusque for 'normal') is the on-screen menu option corresponding to the key. Pressing the key selects to utilise 'Normal 2' mode, which volition be described in more detail in section five.
Notation the difference between 'SETUP', the second function of the key, and the carte du jour choice 'Setup'.
Your calculator will now be working in 'Math' mode, and the word Math will be shown near the right-hand side of the meridian of the figurer display, as shown in Figure 4 below. Math way is the recommended way of using your calculator during this course as information technology allows mathematics to be entered and displayed in a like manner to how you would write it on paper.
one.1 Basic calculations
Bones calculations are entered into the calculator in exactly the same order equally they are written on paper, equally demonstrated in the following activity. The calculator displays the calculation that y'all enter. When you press , the answer is displayed at the lesser right of the screen.
Action two Sums, differences, products and quotients
Yous may take noticed that in role (four) of the above activity, the calculation was as well long to fit on the calculator brandish. In such circumstances, the symbols ' 
' or ' 
' appear at the left or right of the display to bespeak that there is more than information in that direction. This information can exist seen by scrolling left or right using the 
and 
keys, which are found at the left and correct sides of the large cursor control push (labelled with the discussion 'REPLAY') located nether the estimator screen.
If you type a very long calculation into your estimator, and so you may see the cursor (which is ordinarily shown as ' 
') change to ' 
'. This ways that y'all are allowed to type only at nearly ten more characters. If yous run into this, yous should break your calculation into smaller parts.
The cursor is a flashing symbol indicating where the next item entered into the calculator volition appear.
1.2 Fractions or decimals?
In Activity i you set your calculator to use Math mode. In this mode, when the result of a adding is not a whole number, it will be displayed every bit a fraction, such as 
, wherever possible.
To obtain the answer in decimal course, you lot need to printing instead of , or you can toggle between the fractional and decimal outputs using the 
key.
Remember, your reckoner is in Math mode if the word Math is shown at the top of the calculator brandish. If your calculator is not in Math manner, repeat the steps of Action 1.
Activity iii Fractions and decimals
Employ your calculator to observe 
in both fractional and decimal forms.
Answer
In Math mode, calculating gives the result 
.
Converting this to a decimal using gives 0.1814671815.
1.four Making corrections
If y'all make a fault when entering a key sequence into the computer, you lot tin use the editing facilities to right your error.
The and keys on the large cursor control button enable you to motility the cursor (shown on the display as ' ') within a calculation on the calculator screen. Characters can and then be inserted at the cursor location simply by pressing the appropriate buttons, and items to the left of the cursor tin can be deleted using the 
central. This tin can exist done either before or after the key has been pressed. To re-evaluate an edited calculation, simply press at any time.
In some circumstances, however, it may exist easiest to carelessness what you lot take typed and offset again, by pressing the 'all clear' key!
If a severe error is made when inbound a adding into the calculator, information technology may forestall the answer being calculated at all, as the calculation may non brand mathematical sense. In such circumstances a 'Syntax Mistake' will be displayed as shown in Figure 6. The Syntax Error screen gives y'all 2 options:
Other types of calculator fault that you may run across are:
- 'Math Error', when the calculation you entered makes mathematical sense just the result cannot be calculated, such as attempting to divide by nil, or when the result is also large for the calculator to handle.
- 'Stack Error', when your calculation is too complex to exist handled in 1 go – in such circumstances, effort to intermission the adding into a number of simpler ones.
Section 4 considers how you might do this.
In these cases, the reckoner will display a screen similar to that for the Syntax Error, assuasive you to either carelessness or right your calculation.
Activity v Making corrections
Enter the following fundamental sequence into your calculator in an (erroneous) attempt to calculate 
:
What should the correct answer be, and why does this fundamental sequence not requite it?
Employ the computer editing functions to correct the inputted key sequence.
Answer
The correct value of is 16. The key sequence given did not close the bracket before squaring the expression, so merely the 3 was squared, giving 
.
When correcting the expression, be careful to ensure that the cursor is immediately after the 3, and the same meridian as it – shown below – before inserting the missing bracket. Otherwise, the subclass may be inserted within the power.
Figure seven The cursor, placed later the 3
ii Using your estimator for negative numbers
There are ii different mathematical uses for the minus sign (-):
Corresponding to these there are two different minus sign keys on the figurer:
In fact, some calculators permit the 
key to be used for both purposes, but many other calculators require the equivalent of the 
key to be used for negative numbers. For this reason we shall use to input negative numbers throughout this guide.
Note that if you attempt to utilize for subtraction, for case , you will generate a Syntax Error.
Activity half-dozen Subtraction and negative numbers
Yous may have been surprised that the right answer to part (5) is negative. According to the BIDMAS rules, the squaring is performed start, then the negative taken. If we wanted to calculate the square of 
, we write this mathematically as 
and would need to utilize the brackets when evaluating it on a calculator.
3 Using your reckoner for fractions
When your calculator is in Math mode, equally recommended, fractions are entered using the 
push button in the left-hand cavalcade of the office key area of the calculator keypad. This displays a fraction 'template' on the display – as shown in Effigy 8 below – that contains boxes that demand to be 'filled in'. When the button is commencement pressed, the cursor is located in the peak box ready for yous to enter the numerator. To move to the bottom box to enter the denominator, use the cursor down primal 
. If there are farther parts of a calculation to exist entered when the template has been completed, the right cursor central can exist used to motility out of the denominator in preparation for the input of the remainder of the calculation.
Figure 8 A fraction template
Remember, your estimator is in Math manner if the word Math is shown at the meridian of the estimator display. If your reckoner is not in Math manner, repeat the steps of Activity 1.
Mixed numbers such every bit 
can be entered similarly using the mixed number template obtained using the cardinal sequence 
. This template provides three boxes to make full, one for the whole number part, and ane each for the numerator and denominator of the partial part.
Whatever fractional answers to calculations volition automatically be displayed in lowest terms.
Activeness 7 Fractions
Use your computer to:
- express
in its simplest class - summate
of 190.
Yous may have noticed that the results of both these exercises were displayed on the calculator as top-heavy fractions. This is the default behaviour of the figurer in Math style. You tin can toggle between a top-heavy fraction and its mixed number equivalent using the cardinal sequence 
.
The default behaviour of the computer can be changed as follows:
Here, the key is used to admission part of the on-screen bill of fare that is not initially visible.
Action eight Mixed numbers
Use your calculator to:
- limited as a mixed number in its simplest form
- express
equally a height-heavy fraction.
4 Doing longer calculations using your estimator
The volume of wood (in cubic metres) contained in a log of length 
metres with a distance around its middle of 
metres is given by the formula
For a log of length 1.5 grand with a distance around the middle of 92 cm, this becomes
In this section we consider several dissimilar approaches that can be used to evaluate this and other more complex expressions using different functions on your estimator. While the first method – considered in Activity 9 – is probably the most straightforward for this relatively elementary expression, it is useful to see how you might utilise other figurer functions when you are faced with more complicated expressions to evaluate.
The expression for the volume of wood requires the value of 
. Y'all could enter an estimate value for by manus, but this is fourth dimension-consuming and may be prone to error. The calculator has an approximation for built into it, which is obtained using the key sequence 
.
The primal is located on the bottom row of the keypad.
Activity ix Using the fraction primal
The nearly obvious way of computing 
is to enter it equally a fraction on your calculator.
What key sequence is needed, and what is the final answer to 3 significant figures?
Another way to carry out the calculation in Activity 9 is to use the 
key.
Activity 10 Using the primal
Yous volition not obtain the right answer to the calculation
if you blazon
into your calculator and printing . Tin can you explain why? Insert a pair of brackets into the expression with the ÷ sign so that it volition requite the correct answer. So type this new expression into the reckoner and check that yous obtain the same answer as in the activity above.
4.1 Reusing a previous result
An alternative approach to our calculation is to calculate the denominator of the fraction showtime, and and then divide the numerator by this.
You could write down the respond to the showtime part of the calculation on paper, and enter it into the calculator again. Withal, it is possible that y'all may make an error either in writing down the number or in typing it into the calculator. A better method is to use the fact that the calculator retains the terminal calculated reply, which can and then exist inserted in the subsequent calculation using the 
key located at the bottom of the keypad.
Notation that the key only remembers the result of your last calculation.
Activity 11 Bottom first!
Use your calculator to summate the value of the denominator of 
, then complete the calculation by finding the value of 
to iii significant figures.
Answer
The value of the denominator is 12.566…, and the concluding answer is 0.101 to 3 significant figures.
iv.2 Using the calculator memory
A variation on the above method is to break the calculation into two parts, and use the retentiveness functions of the calculator to store the result of the first function. The calculator retentivity is particularly useful when you desire to calculate the values of several expressions that take a common office. This mutual part need be entered only once and its value reused several times subsequently. For example, rewriting the formula for the volume of woods independent in a log as
we tin encounter that no matter what the values of and , the formula always requires the value of 
. If we wished to calculate the volume of wood contained in several unlike logs, it might be efficient to summate the value of once, store it in retentiveness and reuse this value in the subsequent calculations.
The computer has several different memories. We shall first consider the 'G' retentiveness, which is accessed using the 
key (and its associated functions) at the bottom right-mitt corner of the function key area.
Before using the calculator retention, it is skilful practice to ever articulate any previous information stored in the computer using the key sequence (CLR) (Memory) (Yes) .
Annotation that this clears all the figurer memories.
To store the result of an expression only calculated (i.eastward. an reply displayed in the output area of the reckoner screen) in the 'M' computer retention, use the key sequence 
(STO) (1000). Here we are using the second role of the (or recall) button, which is chosen 'STO' (or store). After selecting the store function, we need to tell the calculator which memory the value is to be stored in. These memories are labelled in red on some of the figurer keys, and the 'Thou' retentiveness is obtained by pressing the key. Nosotros could read the cardinal sequence equally 'shop the current effect into the Grand memory'.
To brandish the electric current contents of the 'M' retention, printing (M). The value stored in memory can also be used as part of a subsequent calculation by inserting the 'letter' M into the appropriate indicate of the expression using (M). For example, to find the foursquare of the value currently stored in the 'M' memory, 
, we can employ the primal sequence (M) .
When in that location is a value stored in the 'M' memory, the display indicator Thousand is shown at the height of the display.
Activity 12 Using memory
Shop the value of in the 'M' memory of the calculator and and so use this stored value to evaluate 
to 3 significant figures.
four.iv Other memories
The estimator also has vi other memories, labelled 'A', 'B', 'C', 'D', 'Ten' and 'Y', which are accessed using several of the keys in the lower one-half of the function key area of the calculator. Each memory name is printed in red above the fundamental used to access it.
These memories tin can exist used in exactly the same way as the 'K' memory, except that in that location are no equivalents to the 'add together to memory' ( ) and 'subtract from memory' ( (M-)) functions, and no display indicators.
5 Scientific annotation on your figurer
Displaying numbers in scientific notation on your calculator
If the issue of a calculation is a number greater than or equal to 
(i.east. 
), the calculator will automatically brandish the result using scientific notation. For example, calculating 
gives the answer
,
which is displayed on the calculator screen equally information technology is written here.
Small numbers are also automatically displayed using scientific notation. However, how minor the number needs to be for this to happen depends on the mode the computer is working in:
'Norm' is short for 'normal'.
In Activity 1 you will have already set your calculator to use Norm 2 mode, and nosotros suggest that for the moment you lot continue to apply this. To modify the fashion, use the fundamental sequence (SETUP) (Norm) followed by (for Norm 1) or (for Norm 2).
You lot can also set the calculator to e'er display results using scientific notation with a set number of significant figures using the key sequence (SETUP) 
(Sci) followed by the number of significant figures required, for example . When your calculator is set in this fashion, the display indicator SCI is displayed at the peak of the screen. To cancel such a setting, use one of the key sequences given above to render to a 'Norm' mode.
half-dozen Powers and surds on your calculator
Inputting fractional and negative powers
In Activity 4 you saw how to use the 
key to input powers on the calculator. The key tin can be used with other functions, such as the fraction template , to calculate fractional and negative powers.
Activity 14 Calculating more powers
6.2 Inserting a missing root
Sometimes when entering into your calculator an expression involving roots, you may accidentally forget to press the advisable function central. Even so, moving the cursor to the correct point and pressing the missing primal, every bit in department 1, will not work every bit this simply inserts an empty template.
If yous wish to edit an expression to insert a missing root, first motility the cursor to the right place – that is, to the left of the number. And then actuate the 'Insert' function by pressing (INS), and finally printing the advisable root cardinal.
7 Trigonometric ratios on your reckoner
There are various unlike units in which an angle tin be measured, degrees being one of the possibilities. Before using your figurer to find the values of the trigonometric ratios of angles measured in degrees, you need to ensure that it is set to utilize the right units.
Always bank check that your calculator is using the right system of angle measurement before using trigonometric ratios.
Your reckoner is prepare to apply degrees if the display indicator 
is shown at the height of the screen. If yous meet the indicator 
or 
, then your calculator is set to use different units for measuring angles.
Figure 9 The degrees setting
To set your reckoner to work in degrees, use the key sequence (SETUP) (Deg).
To calculate the sine, cosine or tangent of an bending, press the 
, 
or 
key then blazon in the size of the bending. Note that the , and keys automatically open a bracket for y'all. If yous are simply calculating the sine, cosine or tangent of an angle, only printing after entering the angle – in that location is no need to close the subclass. If y'all are using these ratios every bit office of a larger calculation, and so yous will demand to remember to close the bracket yourself (by pressing ) earlier inbound the remainder of the calculation.
Activity 16 Trigonometric ratios on your calculator
You lot will notice from the answer to part (3) that the calculator displays the ratios of some angles as fractions, involving surds where needed, and not in decimal grade.
nine Radians on your calculator
Your calculator can be set to calculate trigonometric functions using the radian mensurate for angles, instead of degrees, past using the primal sequence (SETUP) 
(Rad).
When in this mode, the display indicator is shown.
Activity 18 Radians on your calculator
Find from the final example in this activity that where an answer is a unproblematic (perchance fractional) multiple of , the respond is displayed in terms of rather than equally a decimal number.
12 Computer reference guide
Estimator modes
General modes
The estimator can operate in several different modes:
- COMP, which is used for general calculations
- STAT, which is used for statistical calculations
- Tabular array, which is used for generating tables of numbers.
COMP is short for 'computation', and STAT is short for 'statistics'.
Comp way is selected by using the key sequence (COMP).
Mathematics modes
At that place are two different means in which mathematics tin can be input to and displayed on the calculator:
Put simply, an irrational number is ane that cannot be expressed as a uncomplicated fraction.
You know that you are in Math mode if the word Math is shown about the right-hand side of the summit of the estimator display. If this is not shown, y'all are using Linear mode.
In Math mode, y'all can force an answer to be displayed as a decimal using , or you lot can toggle betwixt the mathematical and decimal outputs using .
Fraction display modes
It is possible to gear up the calculator so that answers that are top-heavy fractions (such as 
) are always displayed as mixed numbers (such equally ).
Decimal display modes
The calculator can exist ready to brandish decimal numbers in diverse different ways:
12.1 Brandish indicators
These are symbols shown on the figurer display to indicate its electric current state of operation.
| Symbol on display | Meaning |
|---|---|
| | The |
| | The |
| M | A value is stored in the 'M' retention. |
| STO | The Shop key ( |
| RCL | The Retrieve ( |
| | The calculator is set to mensurate angles in degrees. |
| | The reckoner is ready to measure angles in radians. |
| | The reckoner is gear up to measure out angles in gradians. |
| Prepare | The computer is prepare to display answers to a fixed number of decimal places. |
| SCI | The estimator is ready to brandish answers in scientific notation with a stock-still number of significant figures. |
| Math | The calculator is ready to use Math style for input and display. |
| STAT | The calculator is in statistics mode. |
| | There is more data available than can exist displayed, and this tin can be accessed using the upwards/down cursor keys. |
| | The line displayed is longer than tin fit on the display. Other parts of the line can be displayed past scrolling using the left/right cursor keys: |
12.2 Mutual operations
The A, B, C, D, 10, Y memories are used similarly to the Thousand retentiveness, except that these have no 'add together to' and 'subtract from' functions.
12.three Entering mathematics
and 
are mathematical constants.
When using trigonometric functions, ensure that your estimator is ready to employ the right units: degrees or radians.
and 
are calculated in a similar way to 
.
Decision
This free form provided an introduction to studying Mathematics and Statistics. It took you through a series of exercises designed to develop your arroyo to study and learning at a altitude and helped to meliorate your confidence as an independent learner.
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Acknowledgements
Grateful acknowledgement is fabricated to the post-obit:
Course image: kaboompics.com in Pexels made available nether Creative Commons Public Domain one.0 Licence.
Figure 1: © Casio Electronics Co Ltd.
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