How Do You Plug in the Answer Again on the Calculator

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Using a scientific estimator

Introduction

The course describes some of the primary features of a scientific calculator and encourages you to use your calculator, both for everyday arithmetics and for more complicated calculations that employ the function keys as well. Key sequences, which describe which keys to press, are included in all the activities, so y'all can try out the ideas straightaway.

Due to the wide range of scientific calculators available, for the purposes of this course nosotros will be concentrating on the Casio fx-83ES model. Other calculators may function differently to the methods described within this course.

This calculator is used on the Open up Academy courses Starting with maths (Y182) and Discovering mathema t ics (MU123), but would also exist useful for many other courses requiring the use of a scientific reckoner.

This OpenLearn class is an adapted extract from the Open University course MU123 Discovering Mathematics.

Learning outcomes

After studying this class, you lot should be able to:

• understand the basic functions on your estimator

• sympathise which figurer functions are needed for a given problem

• sympathize what may go incorrect when inbound calculations and know how to fix them

• apply knowledge of calculator functions to a range of mathematical calculations.

1 Getting to know your reckoner

The first 11 sections describe how to use the calculator and how to perform different types of calculations. Section 12 contains a estimator reference guide that you can refer to every bit needed for some of the chief key sequences.

This course is not an exhaustive list of all the figurer'due south features. If you are using a different calculator, you should apply the corresponding features of your own calculator to exercise the activities in this guide. Y'all may need to refer to your calculator transmission to do this.

You may be able to download the manual for your computer 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 can understand the data on the display.

Figure ane shows the different parts of the Casio fx-83ES calculator.

Figure ane A typical scientific reckoner

If you are using a dissimilar model of calculator, brand sure that yous can identify similar functions on your model.

The calculator is switched on using the key at the top right-hand 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 cardinal 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 addition, subtraction, partitioning and multiplication, and the key, which is pressed when you want the calculator to display the result of the calculation you take entered. The keys used to insert brackets into a calculation are in the centre of the row above the number keys.

Many keys on the calculator take more than one use. The main part of a central is printed in white on the central itself. The second function of the key is printed in yellow above the key, and is accessed by pressing the button before pressing the cardinal. When you lot press the button, the symbol ' ' appears at the top left-paw corner of the estimator display to remind you lot that the push has been pressed. It disappears when y'all printing another key. Some keys also take a tertiary function, printed in a higher place the cardinal in red. These functions allow numerical values stored in the reckoner memories to be used within calculations and are accessed by pressing the push before the advisable key. When the push is pressed, the symbol ' ' is shown at the top of the calculator display. Y'all will acquire how to utilise the calculator memories later in section four.

The calculator transmission describes this second office as the 'alternating' role of the central.

Some calculator operations are accessed through a organization of menus that are displayed on the computer screen, equally shown in Figure 3. The required menu option is selected by pressing the number central associated with the option, as given on the calculator screen.

Figure iii A typical calculator on-screen menu

When describing how to use various figurer functions, this guide gives the exact keys that you demand to press using the symbols shown on the keys. This is known as a 'key sequence'. If the primal sequence accesses the 2d function of a key, or a function from a menu, the proper name of this function will be given in brackets at the appropriate point in the primal sequence. Names in brackets are thus not keys that you printing but simply describe the function that is accessed using the previous key sequence. For example, to turn off the calculator, press (OFF). In this notation, (OFF) is non a key that you press, but is the proper noun of the 2d role of the key, which is accessed with the key.

The calculator has many modes of operation that impact how mathematics is entered and displayed. These will be described later in this guide, but earlier progressing whatever further you should reset your calculator to the default course settings.

Activity 1 Initialising your calculator

To initialise your calculator to the default course settings, turn information technology on and so enter the following two key sequences:

(CLR) (Setup) (Yes)

(SETUP) (Norm)

Note that in the first cardinal sequence, 'CLR' (which is curt for 'clear') is the 2nd function of the key, and 'Setup' is the name of the on-screen menu pick corresponding to the fundamental. 'Yes' is the name of the on-screen carte option corresponding to the key. This central sequence clears all previous 'setup' settings on the calculator.

In the second key sequence, 'SETUP' is the name of the 2d function of the key, and 'Norm' (short for 'normal') is the on-screen menu option corresponding to the key. Pressing the key selects to use 'Normal 2' mode, which will be described in more detail in department v.

Note the difference between 'SETUP', the second function of the cardinal, and the card option 'Setup'.

Your computer volition now be working in 'Math' way, and the word Math will exist shown near the right-hand side of the summit of the calculator brandish, every bit shown in Figure 4 below. Math mode is the recommended manner of using your calculator during this course as it allows mathematics to be entered and displayed in a similar way to how y'all would write it on newspaper.

i.1 Basic calculations

Bones calculations are entered into the computer in exactly the aforementioned order as they are written on paper, as demonstrated in the post-obit activity. The computer displays the calculation that you enter. When y'all press , the answer is displayed at the bottom right of the screen.

Activeness 2 Sums, differences, products and quotients

You may have noticed that in office (4) of the to a higher place activity, the calculation was also long to fit on the calculator display. In such circumstances, the symbols ' ' or ' ' appear at the left or right of the brandish to point that there is more information in that direction. This information can be seen past scrolling left or correct using the and keys, which are found at the left and right sides of the large cursor control button (labelled with the discussion 'REPLAY') located under the calculator screen.

If you blazon a very long calculation into your calculator,  and so you may see the cursor  (which is usually shown as ' ') alter to ' '. This means that yous are allowed to type only at most 10 more characters. If you see this, yous should break your calculation into smaller parts.

The cursor is a flashing symbol indicating where the next particular entered into the calculator volition appear.

ane.ii Fractions or decimals?

In Activity 1 you set upwardly your calculator to utilise Math mode. In this mode, when the result of a adding is not a whole number, it will be displayed as a fraction, such as , wherever possible.

To obtain the answer in decimal class, you need to press instead of , or you can toggle betwixt the partial and decimal outputs using the key.

Remember, your figurer is in Math mode if the discussion Math is shown at the peak of the calculator display. If your calculator is not in Math mode, repeat the steps of Activity 1.

Activeness 3 Fractions and decimals

Use your calculator to detect in both partial and decimal forms.

Answer

In Math mode, calculating gives the result .

Converting this to a decimal using gives 0.1814671815.

one.iv Making corrections

If you make a mistake when entering a cardinal sequence into the figurer, yous tin can use the editing facilities to right your error.

The and keys on the large cursor control button enable you to motion the cursor (shown on the brandish as ' ') within a calculation on the calculator screen. Characters can and then exist inserted at the cursor location just by pressing the advisable buttons, and items to the left of the cursor tin be deleted using the key. This can be done either earlier or after the key has been pressed. To re-evaluate an edited adding, simply press at whatsoever time.

In some circumstances, however, information technology may be easiest to abandon what you take typed and kickoff again, by pressing the 'all articulate' key!

If a severe error is made when inbound a calculation into the calculator, it may prevent the respond existence calculated at all, equally the calculation may not brand mathematical sense. In such circumstances a 'Syntax Mistake' volition exist displayed as shown in Effigy 6. The Syntax Mistake screen gives yous two options:

Other types of reckoner fault that y'all may encounter are:

• 'Math Error', when the calculation you lot entered makes mathematical sense but the result cannot be calculated, such as attempting to divide by zero, or when the result is too large for the calculator to handle.
• 'Stack Error', when your calculation is as well complex to be handled in one become – in such circumstances, try to pause the calculation into a number of simpler ones.

Section iv considers how you lot might do this.

In these cases, the calculator will display a screen similar to that for the Syntax Fault, assuasive you to either carelessness or correct your calculation.

Activity five Making corrections

Enter the post-obit cardinal sequence into your calculator in an (erroneous) effort to calculate :

What should the correct answer exist, and why does this cardinal sequence not give it?

Utilise the calculator editing functions to correct the inputted key sequence.

Respond

The correct value of is xvi. The key sequence given did not close the bracket before squaring the expression, and then just the 3 was squared, giving .

When correcting the expression, be careful to ensure that the cursor is immediately after the 3, and the same acme as it – shown below – before inserting the missing bracket. Otherwise, the bracket may exist inserted inside the power.

Effigy vii The cursor, placed after the 3

2 Using your computer for negative numbers

In that location are two different mathematical uses for the minus sign (-):

Respective to these in that location are ii unlike minus sign keys on the calculator:

In fact, some calculators permit the key to be used for both purposes, but many other calculators crave the equivalent of the central to be used for negative numbers. For this reason we shall use to input negative numbers throughout this guide.

Note that if yous attempt to use for subtraction, for example , you will generate a Syntax Mistake.

Activeness 6 Subtraction and negative numbers

You may take been surprised that the correct answer to part (5) is negative. According to the BIDMAS rules, the squaring is performed kickoff, then the negative taken. If we wanted to calculate the square of , we write this mathematically every bit and would need to use the brackets when evaluating it on a calculator.

3 Using your calculator for fractions

When your estimator is in Math style, every bit recommended, fractions are entered using the button in the left-mitt column of the function fundamental expanse of the calculator keypad. This displays a fraction 'template' on the brandish – every bit shown in Figure viii beneath – that contains boxes that need to be 'filled in'. When the button is starting time pressed, the cursor is located in the tiptop box ready for you lot to enter the numerator. To move to the bottom box to enter the denominator, use the cursor down key . If in that location are farther parts of a adding to be entered when the template has been completed, the right cursor key can exist used to move out of the denominator in preparation for the input of the rest of the calculation.

Figure 8 A fraction template

Remember, your calculator is in Math manner if the discussion Math is shown at the top of the calculator display. If your reckoner is not in Math mode, echo the steps of Activity 1.

Mixed numbers such equally tin can exist entered similarly using the mixed number template obtained using the key sequence . This template provides 3 boxes to fill, 1 for the whole number part, and 1 each for the numerator and denominator of the fractional office.

Whatever fractional answers to calculations will automatically be displayed in lowest terms.

Activity 7 Fractions

Use your estimator to:

1. express in its simplest class
2. summate of 190.

You may accept 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 mode. You can toggle between a top-heavy fraction and its mixed number equivalent using the cardinal sequence .

The default behaviour of the reckoner can be inverse as follows:

Here, the key is used to access part of the on-screen card that is not initially visible.

Activity viii Mixed numbers

Use your estimator to:

1. express equally a mixed number in its simplest class
2. express equally a top-heavy fraction.

iv Doing longer calculations using your figurer

The volume of wood (in cubic metres) contained in a log of length metres with a altitude around its center of metres is given by the formula

For a log of length one.5 m with a distance around the center of 92 cm, this becomes

In this section we consider several dissimilar approaches that tin can be used to evaluate this and other more circuitous expressions using dissimilar functions on your computer. While the first method – considered in Activity nine – is probably the most straightforward for this relatively elementary expression, it is useful to run into how you might utilize other calculator functions when you are faced with more than complicated expressions to evaluate.

The expression for the volume of forest requires the value of . Yous could enter an approximate value for by hand, but this is fourth dimension-consuming and may be prone to error. The computer has an approximation for built into it, which is obtained using the central sequence .

The primal is located on the bottom row of the keypad.

Activity 9 Using the fraction central

The virtually obvious way of calculating is to enter it as a fraction on your calculator.

What key sequence is needed, and what is the final answer to 3 significant figures?

Another way to comport out the calculation in Activity 9 is to utilise the fundamental.

Activeness 10 Using the cardinal

Y'all will non obtain the correct answer to the calculation

if y'all type

into your calculator and press . Can you explicate why? Insert a pair of brackets into the expression with the ÷ sign so that it volition give the correct answer. So type this new expression into the calculator and check that you lot obtain the same respond as in the action above.

4.1 Reusing a previous result

An culling approach to our calculation is to summate the denominator of the fraction get-go, then split up the numerator past this.

You could write down the respond to the showtime office of the calculation on newspaper, and enter it into the computer again. Yet, it is possible that you may brand 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 final calculated respond, which tin can then be inserted in the subsequent calculation using the key located at the bottom of the keypad.

Note that the primal only remembers the event of your last adding.

Activity 11 Lesser first!

Use your reckoner to calculate the value of the denominator of , then complete the calculation by finding the value of to 3 pregnant figures.

Answer

The value of the denominator is 12.566…, and the final answer is 0.101 to three significant figures.

four.ii Using the reckoner memory

A variation on the to a higher place method is to suspension the calculation into two parts, and use the retention functions of the calculator to store the issue of the beginning part. The calculator memory is specially useful when you want to calculate the values of several expressions that have a mutual function. This common part need be entered simply one time and its value reused several times subsequently. For case, rewriting the formula for the volume of forest contained in a log equally

nosotros can see that no affair what the values of and , the formula always requires the value of . If we wished to summate the volume of wood contained in several different logs, information technology might be efficient to calculate the value of in one case, shop it in retentivity and reuse this value in the subsequent calculations.

The estimator has several different memories. We shall start consider the 'Thousand' retention, which is accessed using the key (and its associated functions) at the bottom correct-hand corner of the function fundamental surface area.

Earlier using the calculator retention, it is practiced practice to ever clear any previous data stored in the calculator using the cardinal sequence (CLR) (Retentivity) (Yes) .

Note that this clears all the reckoner memories.

To shop the result of an expression just calculated (i.e. an answer displayed in the output area of the calculator screen) in the 'M' calculator retentiveness, use the key sequence (STO) (M). Here nosotros are using the second function of the (or recall) push button, which is called 'STO' (or shop). Afterwards selecting the store function, nosotros need to tell the calculator which memory the value is to be stored in. These memories are labelled in blood-red on some of the calculator keys, and the 'G' retentivity is obtained past pressing the key. We could read the key sequence as 'shop the current issue into the M memory'.

To display the electric current contents of the '1000' retentiveness, press (M). The value stored in memory tin can also be used as office of a subsequent adding by inserting the 'letter' K into the appropriate point of the expression using (Chiliad). For example, to notice the square of the value currently stored in the 'Grand' memory, , nosotros tin use the cardinal sequence (G) .

When there is a value stored in the 'Chiliad' retentivity, the brandish indicator M is shown at the top of the brandish.

Activity 12 Using retention

Store the value of in the '1000' retentiveness of the calculator and and then use this stored value to evaluate to 3 significant figures.

iv.4 Other memories

The calculator too has half-dozen other memories, labelled 'A', 'B', 'C', 'D', 'Ten' and 'Y', which are accessed using several of the keys in the lower half of the role key area of the calculator. Each retention name is printed in red above the key used to access it.

These memories can be used in exactly the same way every bit the 'Thousand' retentivity, except that there are no equivalents to the 'add to memory' ( ) and 'subtract from memory' ( (M-)) functions, and no brandish indicators.

v Scientific notation on your reckoner

Displaying numbers in scientific notation on your calculator

If the result of a calculation is a number greater than or equal to (i.e. ), the estimator volition automatically display the event using scientific notation. For example, computing gives the respond

,

which is displayed on the figurer screen every bit it is written here.

Pocket-size numbers are also automatically displayed using scientific notation. All the same, how small the number needs to be for this to happen depends on the mode the calculator is working in:

'Norm' is short for 'normal'.

In Activity i y'all will have already fix your calculator to apply Norm two mode, and nosotros advise that for the moment you continue to use this. To change the mode, use the primal sequence (SETUP) (Norm) followed by (for Norm ane) or (for Norm 2).

Yous can besides set the calculator to e'er display results using scientific notation with a set up number of meaning figures using the key sequence (SETUP) (Sci) followed by the number of significant figures required, for example . When your calculator is set in this manner, the brandish indicator SCI is displayed at the top of the screen. To cancel such a setting, use one of the fundamental sequences given above to return to a 'Norm' mode.

6 Powers and surds on your calculator

Inputting fractional and negative powers

In Action 4 you saw how to use the key to input powers on the computer. The key can exist used with other functions, such as the fraction template , to calculate partial and negative powers.

Action 14 Calculating more powers

6.2 Inserting a missing root

Sometimes when entering into your reckoner an expression involving roots, yous may accidentally forget to press the advisable function key. However, moving the cursor to the correct point and pressing the missing key, as in section 1, will not work as this merely inserts an empty template.

If you wish to edit an expression to insert a missing root, first move the cursor to the correct place – that is, to the left of the number. Then activate the 'Insert' function by pressing (INS), and finally press the appropriate root key.

7 Trigonometric ratios on your reckoner

At that place are various different units in which an angle can be measured, degrees being 1 of the possibilities. Before using your calculator to notice the values of the trigonometric ratios of angles measured in degrees, yous need to ensure that it is ready to use the correct units.

E'er check that your calculator is using the correct system of bending measurement before using trigonometric ratios.

Your calculator is set to use degrees if the display indicator is shown at the top of the screen. If yous come across the indicator or , so your calculator is set to use unlike units for measuring angles.

Figure nine The degrees setting

To set your computer to work in degrees, use the key sequence (SETUP) (Deg).

To calculate the sine, cosine or tangent of an bending, printing the , or key and then type in the size of the bending. Note that the , and keys automatically open a bracket for you. If you are simply calculating the sine, cosine or tangent of an angle, just press after entering the angle – there is no need to close the bracket. If y'all are using these ratios as part of a larger calculation, then you volition need to remember to close the subclass yourself (past pressing ) before entering the residuum of the calculation.

Action sixteen Trigonometric ratios on your calculator

You will notice from the answer to function (three) that the reckoner displays the ratios of some angles every bit fractions, involving surds where needed, and not in decimal class.

ix Radians on your calculator

Your calculator can exist set to summate trigonometric functions using the radian mensurate for angles, instead of degrees, by using the central sequence (SETUP) (Rad).

When in this mode, the display indicator is shown.

Activity 18 Radians on your figurer

Notice from the final instance in this activity that where an answer is a elementary (possibly fractional) multiple of , the answer is displayed in terms of rather than as a decimal number.

12 Calculator reference guide

Calculator modes

General modes

The calculator can operate in several different modes:

• COMP, which is used for general calculations
• STAT, which is used for statistical calculations
• Table, which is used for generating tables of numbers.

COMP is short for 'computation', and STAT is brusk for 'statistics'.

Comp way is selected by using the central sequence (COMP).

Mathematics modes

There are two different ways in which mathematics can be input to and displayed on the calculator:

Put simply, an irrational number is 1 that cannot be expressed every bit a uncomplicated fraction.

You lot know that you are in Math mode if the word Math is shown most the right-hand side of the meridian of the calculator display. If this is non shown, you are using Linear mode.

In Math mode, you can force an answer to be displayed as a decimal using , or you can toggle between the mathematical and decimal outputs using .

Fraction brandish modes

It is possible to set the figurer so that answers that are top-heavy fractions (such as ) are e'er displayed as mixed numbers (such equally ).

Decimal display modes

The computer tin exist set to brandish decimal numbers in diverse different means:

12.1 Brandish indicators

These are symbols shown on the calculator display to indicate its electric current state of operation.

Symbol on brandish	Significant
	The central has been pressed.
	The key has been pressed.
M	A value is stored in the 'G' memory.
STO	The STORE key ( (STO)) has been pressed.
RCL	The RECALL ( ) fundamental has been pressed.
	The reckoner is set to measure angles in degrees.
	The computer is gear up to measure angles in radians.
	The calculator is set to mensurate angles in gradians.
FIX	The calculator is gear up to display answers to a fixed number of decimal places.
SCI	The calculator is prepare to display answers in scientific notation with a stock-still number of significant figures.
Math	The reckoner is set up to use Math manner for input and brandish.
STAT	The reckoner is in statistics fashion.
	At that place is more information available than can be displayed, and this can be accessed using the up/down cursor keys.
	The line displayed is longer than can fit on the display. Other parts of the line tin can be displayed by scrolling using the left/correct cursor keys: and .

12.2 Common operations

The A, B, C, D, X, Y memories are used similarly to the M memory, except that these have no 'add to' and 'decrease from' functions.

12.iii Entering mathematics

and are mathematical constants.

When using trigonometric functions, ensure that your reckoner is ready to use the right units: degrees or radians.

and are calculated in a similar way to .

Conclusion

This free course provided an introduction to studying Mathematics and Statistics. It took you through a series of exercises designed to develop your arroyo to written report and learning at a distance and helped to improve your confidence as an independent learner.

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Acknowledgements

Grateful acknowledgement is fabricated to the following:

Course image: kaboompics.com in Pexels made available under Creative Commons Public Domain ane.0 Licence.

Figure 1: © Casio Electronics Co Ltd.

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