With an arithmetic calculator you enter
2 + 3 × 4 = 20.
On the other hand, if the problem is stated as 2 + (3 × 4) and you are using an algebraic calculator, you must enter
2 + ( 3 × 4 ) = 14.
However, with an arithmetic calculator, enter the problem (2 + 3)
×
4 as2 + 3 × 4 = 14.
From the preceding examples, you can see that it is vital to be familiar with your calculator and know how to properly enter problems into it. With practice, proper calculator operation becomes easy.
UNDERSTANDING CALCULATOR FUNCTIONS
In using a calculator, two important considerations are (1) how to enter the numbers into the calculator and (2) how to tell the calculator which operation to perform. Successful operation of any calculator depends on your reading and following the instructions provided by the manufacturer. Knowing exactly how the calculator functions saves time and frustration and prevents errors.
Basic Operations
Calculators require that you press keys to instruct the calculator to perform. This section describes several keys and shows their symbols in the margin. Be aware, however, that the keys on your calculator may be different. Therefore, use the following discussion to get a basic understanding of the keys, but when using your own calculator, refer to its instructions.
Power Switch. Some calculators have a power switch and some do not. Light-powered models may require that you press an all clear or some other key to turn on the calculator. Light-powered models usually turn off automatically when not in use for a short period. Battery-operated or plug-in models, on the other hand, usually have a power switch. In any case, once you turn on the calculator, it clears the display and erases whatever is stored in the memory unless the calculator has a continuous memory. Calculator memory is discussed shortly. As you will learn, some calculators store what has been put in their memory even after the calculator has been turned off.
Numbers 0–9. Pressing a number key displays the number and enters it in the calculator.
Clear All. Pressing the clear-all key removes, or erases, whatever was in the cal-culator, so a new problem can be started. As mentioned earlier, on some models, this key also turns on the calculator.
Clear Entry or Clear Display. Calculators with this key allow you to clear only the last entry into the calculator. A ce or cd key is handy when entering a large number of figures and you enter a wrong figure after you have already entered
ON/OFF
ON/AC or ON/C
7 8 9
4 5 6
1 2 3
0
C CA or AC CLEAR
CE CE/C or CD
46 THE CALCULATOR
several. By pressing the clear entry key, you merely remove the last entry and not those that preceded it. This function may be combined with the clear-all function for a dual-duty key: touched once, it clears the last entry; touched again, it clears all.
Enter. On RPN calculators, pressing this key either enters the displayed number into the calculator’s memory or yields the answer to the problem. (Sometimes, it is labeled execute or exe.)
Period. Pressing the period on the keyboard inserts a decimal point.
Addition. Pressing the plus key instructs the calculator to add the next entered (or previously entered) quantity to the displayed number.
Subtraction. Pressing the minus key instructs the calculator to subtract the next (or previously entered) quantity to the displayed number.
Multiplication. Pressing the times key instructs the calculator to multiply the displayed number by the next entered quantity.
Division. Pressing the division key instructs the calculator to divide the displayed number by the next entered quantity.
Equals. Pressing the equals key completes the previously entered operation and displays a result. Arithmetic and algebraic calculators use this key. RPN calcula-tors use an entry key.
Percent. This key shifts the decimal point of the number shown in the display two places to the left because (as you will learn later in this manual) percentage is a way of stating a portion of a quantity expressed in hundredths (0.01). In other words, finding 25% of a quantity is the same as multiplying the quantity by 0.25.
Square root. Pressing the square-root key finds the square root of the displayed num ber.
Memory Functions
Most calculators come with a memory. In less expensive models, the memory has only one level, so the calculator can retain only one piece of information. More expensive calculators store many pieces of information when location keys are pressed after the memory key. Information can be stored and recalled at any time.
This section discusses memory functions to give you an idea of their capability.
Just as the basic keys on your calculator may be different, so may the memory keys on your calculator be different from the keys shown here. Therefore, always refer to the instructions that accompany the calculator.
Store in Memory. This key stores a displayed quantity in a specific place, or level, in the memory.
Memory Addition. You can add or subtract a number to a number already in the memory by pressing the add memory key. However, on some calculators, pressing this key stores a number or operation in the memory. On calculators with second and third function keys (see the section on scientific functions), you may have to press two keys to add to the memory.
Memory Subtraction. Pressing this key subtracts the displayed number from a number already stored in the memory. Or, on some calculators, this key clears (erases) any numbers stored in the memory.
ENT or ENTER
Understanding Calculator Functions 47
Memory Multiplication. Pressing this key multiplies a number already stored in the memory by the number shown in the display, leaving the result in the memory.
Memory Division. This key divides the number already stored in the memory by the number shown in the display, leaving the result in the memory.
Recall from Memory. Pressing this key recalls memory contents and displays, but does not change, memory contents.
Clear Memory. This key (some calculators require pressing more than one key) clears numbers stored in memory.
Add to Memory. This key adds a displayed number (negative or positive) to a number in the memory in a specific level. (x and x represent the numbers added.) Multiply By Number in Memory. This key multiplies a displayed number by a number stored in the memory in a specific level.
Exchange. This key swaps the displayed number with that in the memory.
Clear Memory Level. This key clears data stored in a specific level as indicated by its two-digit location number.
Scientific Functions
The scientific, or slide-rule, calculator provides many functions, including trigo-nometric and logarithmic operations. Following are functions found on many scientific calculators. Remember, as always, that calculators are different. So, your calculator may or may not have the keys shown. Or, it may have additional keys that are not illustrated here. What is more, you may have to press a second or third function key to make it work as desired. Therefore, you must use and refer to the instructions that come with the calculator and become familiar with the calculator’s operation and keys.
Second Function Key. This key allows you to gain access to a key’s second func-tion. Put another way, on some calculators, one key performs two functions. To change a key’s function, press the second function key first. Pressing it makes a key assume a different (a second) function. For example, a square-root sign (√) may be on the key itself and a cube-root sign (3√) may be printed on the case just above it. (Or, the second function may be on the key itself, but in letters smaller than the key’s first function.) Pressing the √ key alone gives the square root of the entered number. But, pressing the second function key and then the √ key makes the key function as a cube root (3√) key. Usually, a key’s second function is printed on the key or on the case of the calculator in the same color as the second function key’s color. For example, if the second function key is orange, a key’s second function is also printed in orange.
Third Function Key. As with the second function key, you press this key first to make a key function as desired. For example, the key’s first function may be marked ln, its second function ex, and its third function 3√x. A key’s third func-tion is usually printed on the calculator’s case and the color of the third funcfunc-tion key and the label usually match.
Square. After entering a number, pressing this key squares the number. For example, press 2 , x2, and = . The answer is 4 because 22 is 4.
48 THE CALCULATOR
Reciprocal. Pressing this key calculates and displays the reciprocal of the dis-played number. A reciprocal is a number related to another number by the fact that when the two numbers are multiplied together, the product is 1. For example, the reciprocal of ¹⁄₁₆ is ¹⁶⁄₁ (or 16) because ¹⁄₁₆ × ¹⁶⁄₁ = ¹⁶⁄₁₆, or 1. In the same way, the reciprocal of 4 is ¼, because ⁴⁄₁ × ¼ = 1. One use of the reciprocal key occurs when converting English, or conventional, units of measure to metric units and metric units to English. Suppose, for example, that you know that to convert feet to metres, you multiply the number of feet by 0.3048. However, also suppose that you need to convert metres to feet but that you do not know the conversion factor.
If you know the conversion factor of 0.3048, and your calculator has a reciprocal key, it is easy to determine the factor required to convert metres to feet. Simply enter .3048 and press the reciprocal key to obtain 3.2808. This number is the conversion factor needed to change feet to metres. For example, 9 feet × 0.3048
= 2.7432 metres. Because the reciprocal of 0.3048 is 3.2808, multiply 2.7432 by 3.2808 to obtain 8.9999, or 9 feet. The reciprocal key also has other uses as you will see in Chapter 7, “Trigonometry.”
x–y interchange. After entering a number or obtaining a result, this key changes the order within the calculator so that the number entered first or a previous result is interchanged with that entered second or a displayed result. The ability to interchange entries is useful in solving complex equations.
Parentheses or Brackets. When you press the left parenthesis or bracket, enter an operation, and press the right parenthesis or bracket, the calculator performs the operation within the parentheses or brackets first so that the contents are treated as one unit.
Change Sign. After entering a number, pressing this key changes the sign of the displayed number from positive to negative or vice versa.
Pi. On calculators with a pi sign key (π), pressing this key enters the constant, 3.14159265359, to the number of significant figures allowed by the calculator—
for example, 3.1416 is pi carried to five significant figures, which is sometimes abbreviated as 5 s.f. (Chapter 6 covers the use of pi in calculations.) If your work regularly requires determining the area of circles and spheres, your calculator should have the pi sign. Be aware that not all of them do.
Enter Exponent. Calculators with this key allow a special exponential nota-tion, which is handy for dealing with large numbers. It is easier to express large numbers as powers of 10. For example, 10,000,000, which is ten million, can be expressed as 107. Notice that ten million, or 107, is 1 followed by 7 zeros. So, rais-ing 10 to the 7th power is the same as writrais-ing 1 followed by 7 zeros. Expressrais-ing large numbers by raising a base value to a power makes them easier to write and to deal with. For example, the average distance from the sun to the earth is 93 million (93,000,000) miles. This figure may also be expressed as 9.3 × 107—that is, 93 followed by 6 zeros. On a calculator with an EE or EXE key, enter 9 . 3 EE 7 = 93,000,000. Some calculators allow you to enter an exponent with an yx key, which is discussed below.
Trigonometric Functions. These keys allow you to enter and find trigonometric functions (chapter 7 covers trigonometric functions).
Inverse Trigonometric Functions. These keys calculate the inverse trigonometric functions. (Chapter 7 also covers inverse trigonometric functions). Usually, these keys are accessed after pressing the second function key.
1/x