For example, rewriting the formula for the volume of wood contained in a log as. If we wished to calculate the volume of wood contained in several different logs, it might be efficient to calculate the value of once, store it in memory and reuse this value in the subsequent calculations. The calculator has several different memories. Before using the calculator memory, it is good practice to always clear any previous data stored in the calculator using the key sequence CLR Memory Yes.
To store the result of an expression just calculated i. After selecting the store function, we need to tell the calculator which memory the value is to be stored in.
Once or STO has been pressed, the display indicator RCL or STO is shown on the display to indicate that the calculator is waiting to know which memory to recall store the value from in. The value of which equals 0. This value can then be used to find the final result using M , which gives 0. Expressions can also be stored in, added to or subtracted from the memory at the same time as they are evaluated by replacing the at the end of a calculation with one of the memory access sequences.
For example, to calculate and store the result straight into the memory, use the key sequence STO M. Each memory name is printed in red above the key used to access it. If the result of a calculation is a number greater than or equal to i.
For example, calculating gives the answer. Small numbers are also automatically displayed using scientific notation. However, how small the number needs to be for this to happen depends on the mode the calculator is working in:. In Activity 1 you will have already set your calculator to use Norm 2 mode, and we suggest that for the moment you continue to use this. You can also set the calculator to always 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 top of the screen. Numbers expressed in scientific notation can be input directly to the calculator by using the key on the bottom row of keys.
For example, can be entered using the key sequence. Use the scientific notation functions of your calculator to calculate each of the following, giving your answer in both scientific and ordinary forms. In Activity 4 you saw how to use the key to input powers on the calculator. The key can be used with other functions, such as the fraction template , to calculate fractional and negative powers. Calculate each of the following using your calculator, giving your answer correct to 3 significant figures.
Just as there are keys on your calculator for entering powers, roots can also be entered directly. Square roots can be calculated using the key. For example, can be entered using. Cube roots are entered using the second function of this key.
For higher roots, such as fourth or fifth roots you need to use the more general template, which is the second function of the key. This template is filled in by using the number and arrow keys and in a way similar to that used when the fraction template is completed. You will notice from the result of Activity 15, part 4 that the calculator sometimes presents answers using surds.
To find the decimal equivalent of an answer like this, you can use the or keys that you used earlier to find the decimal forms of fractional answers. Sometimes when entering into your calculator an expression involving roots, you may accidentally forget to press the appropriate function key.
However, moving the cursor to the correct point and pressing the missing key, as in section 1, will not work as this simply 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.
There are various different units in which an angle can be measured, degrees being one of the possibilities. Before using your calculator to find the values of the trigonometric ratios of angles measured in degrees, you need to ensure that it is set to use the correct units.
Always check that your calculator is using the correct system of angle 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 you see the indicator or , then your calculator is set to use different units for measuring angles. To calculate the sine, cosine or tangent of an angle, press the , or key and then type in the size of the angle.
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 you are using these ratios as part of a larger calculation, then you will need to remember to close the bracket yourself by pressing before entering the remainder of the calculation.
Some older models of calculator require the angle to be input first, followed by the , or button. Calculate the value of each of the following using your calculator, giving your answers correct to 3 significant figures. If you obtained the answer 0. Note that when entering this expression in your calculator, it is possible to omit explicitly entering the multiplication between the 2 and since the calculator will assume it. Note that means first find the sine of , then square the answer.
The key sequence to enter into the calculator is thus. The first is necessary to close the bracket automatically opened when pressing , and the second closes the bracket opened at the start of the sequence. Since the calculator evaluates the sine as soon as it encounters the first closing bracket, it is possible to enter this expression using the alternative sequence , but this is not recommended as the former is more clear.
It is a property of trigonometric ratios that for any angle ,. You 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 form.
The decimal form can be found using or. Inverse trigonometric values can be found using the second functions , and of the , and keys. These functions are used in a similar manner to , and. Calculate the value of each of the following expressions using your calculator, where possible, giving your answers correct to 1 decimal place. If you obtained the answer or 0. Make sure that you are working in degrees. In part 1 of the activity above, you used your calculator to find an angle whose sine is 0.
This is not the only angle whose sine is 0. Similar remarks apply to parts 2 and 3. Your calculator can be set to calculate trigonometric functions using the radian measure for angles, instead of degrees, by using the key sequence SETUP Rad.
When in this mode, the display indicator is shown. In this activity, the angles are measured in radians. Find the values of the following expressions, giving your answers correct to 3 significant figures. Remember: can be input to the calculator using. Notice from the final example in this activity that where an answer is a simple possibly fractional multiple of , the answer is displayed in terms of rather than as a decimal number.
Logarithms to base 10 of numbers can be found using the key. For example, can be calculated using the key sequence. Note that as with the trigonometric functions, the key automatically opens a bracket that must be closed if you are using the calculated logarithm as part of a longer calculation.
The second function of the key , accessed using , can be used as an alternative to when calculating powers of All the calculations are logarithms to base 10, so we use the key. Natural logarithms, for example , can be evaluated on your calculator using the key.
The second function of this key permits the calculation of powers of. Note that an approximate value for itself can be obtained using the key sequence. Remember that means the same as ln. Some calculators have a key instead of. Calculate the value of each of the following using your calculator, giving each answer to 3 significant figures.
Notice that this is about three times the answer to part 2. In fact, the exact value of is precisely three times the exact value of. This is because , and for any base of logarithm,. This is an important result for logarithms. In this case we have. To calculate this answer correctly, you need to remember to close the bracket after the 3 on your calculator display. Comp mode is selected by using the key sequence COMP.
There are two different ways in which mathematics can be input to and displayed on the calculator:. You know that you are in Math mode if the word Math is shown near the right-hand side of the top of the calculator display. If this is not 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. It is possible to set the calculator so that answers that are top-heavy fractions such as are always displayed as mixed numbers such as.
The key has been pressed. The line displayed is longer than can fit on the display. CLR Memory Yes. CLR All Yes. STO M. Set answers to be displayed to 3 decimal places To use a different number of decimal places, replace with that number.
Set answers to be displayed in scientific notation with 3 significant figures To use a different number of significant figures, replace with that number. In Math mode:. In Linear mode:. When using trigonometric functions, ensure that your calculator is set to use the correct units: degrees or radians. This free course provided an introduction to studying Mathematics and Statistics. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.
Course image: kaboompics. If reading this text has inspired you to learn more, you may be interested in joining the millions of people who discover our free learning resources and qualifications by visiting The Open University - www.
Printable page generated Friday, 12 Nov , Use 'Print preview' to check the number of pages and printer settings. Print functionality varies between browsers. Printable page generated Friday, 12 Nov , Using a scientific calculator Introduction The course describes some of the main features of a scientific calculator and encourages you to use your calculator, both for everyday arithmetic and for more complicated calculations that use the function keys as well.
Learning outcomes After studying this course, you should be able to: understand the basic functions on your calculator understand which calculator functions are needed for a given problem understand what may go wrong when entering calculations and know how to fix them apply knowledge of calculator functions to a range of mathematical calculations.
Figure 1 A typical scientific calculator. Figure 2 The calculator display. Figure 3 A typical calculator on-screen menu. Activity 2 Sums, differences, products and quotients Use your calculator to work out the answers to the following calculations.
Activity 3 Fractions and decimals Use your calculator to find in both fractional and decimal forms. Answer In Math mode, calculating gives the result. Figure 5 The general power key function. Activity 4 Calculating powers Calculate each of the following using your calculator.
Answer Here you need to use the general power key. The Syntax Error screen gives you two options: Press to abandon the calculation and clear the screen press either or to return to the erroneous calculation with the editing cursor placed at the point of the error, ready for a correction to be made Figure 6 Syntax Error.
Section 4 considers how you might do this. Activity 5 Making corrections Enter the following key sequence into your calculator in an erroneous attempt to calculate : What should the correct answer be, and why does this key sequence not give it?
Use the calculator editing functions to correct the inputted key sequence. Answer The correct value of is Figure 7 The cursor, placed after the 3. Corresponding to these there are two different minus sign keys on the calculator: , which is used for the operation of subtraction, as in , which is used for negative numbers, e.
Activity 6 Subtraction and negative numbers Calculate each of the following using your calculator. Answer Remember to press to obtain a decimal answer. Figure 8 A fraction template. Activity 7 Fractions Use your calculator to: express in its simplest form calculate of Answer of can be written , which is equal to or Activity 8 Mixed numbers Use your calculator to: express as a mixed number in its simplest form express as a top-heavy fraction.
Answer Remember to use to toggle between the top-heavy fraction and mixed number answers. Activity 9 Using the fraction key The most 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? Answer to 3 significant figures. Activity 10 Using the key You will not obtain the correct answer to the calculation if you type into your calculator and press. Answer Typing into the calculator and pressing will not give the correct answer because the calculator will follow the BIDMAS rules and divide by 4 and then multiply by , instead of dividing by.
Activity 11 Bottom first! Answer The value of the denominator is For example, rewriting the formula for the volume of wood contained in a log as we can see that no matter what the values of and , the formula always requires the value of. Note that this clears all the calculator memories. Answer The value of which equals 0. To subtract the value of the latest calculation from the value currently in the memory, use the key sequence M-. Activity 13 Calculating with scientific notation Use the scientific notation functions of your calculator to calculate each of the following, giving your answer in both scientific and ordinary forms.
Answer or or 0. Activity 14 Calculating more powers Calculate each of the following using your calculator, giving your answer correct to 3 significant figures. Answer to 3 significant figures using the key sequence. Activity 15 Calculating roots Calculate each of the following using your calculator, giving your answer correct to 3 significant figures.
This is true only if the calculator is in the recommended Math mode. Figure 9 The degrees setting. Activity 16 Trigonometric ratios on your calculator Calculate the value of each of the following using your calculator, giving your answers correct to 3 significant figures. If you got 0. Enter 10, press the exponent key, then press 5 and enter. Before you start making a list of calculations, however, you should do a simple test to make sure your calculator isn't one of those that requires you to input the exponent first.
Enter the number 2, press the exponent key, then enter 3. The display should read 8. If it reads 9, that's because the calculator interpreted the input as 3 2 instead of 2 3. That means you need to enter the exponent before the base. Some calculators have a key marked y x. Some numbers, such as billion, have too many digits to display on a calculator. When this happens, the calculator displays the number in scientific notation, using the letter E to denote 10 to the power of whatever number comes after it.
For example, billion appears on a scientific calculator as 2. You can add, subtract, multiply and divide large numbers just as you would small ones, and the results will continue to appear in scientific notation a long as they continue to have too many digits to display. Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan.
He began writing online in , offering information in scientific, cultural and practical topics. His writing covers science, math and home improvement and design, as well as religion and the oriental healing arts. Negation : This key, denoted by NEG or - turns a positive number into a negative one.
It is different from the subtraction key. Square Root : Denoted by the square root sign, it automatically displays the square root of the number you enter. Natural Logarithm : Denoted by LN, this key displays log e of the number you enter. Angle Functions : Scientific calculators have six keys the display the sine, cosine, tangent and the inverse of each for the number you enter. Natural Exponent : The key, denoted by e x , raises e to the power you enter.
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