Manual / Guide · 1976
TI-30 Owner's Manual (1976)
Texas Instruments' owner's manual for the original LED TI-30 of 1976.
Manual / Guide · 1976
Texas Instruments' owner's manual for the original LED TI-30 of 1976.
Texas Instruments. electronic side-rule calculater: TI-30 OWNER’S MANUAL Copyright © 1976, Texas instruments incorporated Secooaa eae Arc sine, Arc cosine, Arc tangent Degree, Radian, Grad Conversions Hyperbolic Functions... 2... 1-2. inverse Hyperbolic Functions .. 2... . . |. DESCRIPTION Problem solving is an integral part of every field of Study. It is through the solutions of problems that the Critical decisions of business and science are tested and verified. Mastery of those mathematical techniques begins early in school and continues throughout life. The TI-30 slide-rule calculator produces an accurate electronic means of obtaining answers to a wide range of problems beginning with elemental arithmetic and continuing through the most complicated of situations. Use this calculator regularly and it will soon become an inseparable component of your problem solving system. Years of concentrated research in the calculator industry and the latest electronic advances have combined to produce this versatile yet reasonably priced calculator. Here are a few of its features. Features and Functions + Complete Solid-State Circuitry with high quality components. * Sealed Keyboard to minimize dust and moisture accumulation, * Electronic ON and OFF provides for special power- saving features. Only a traveling decimal is teft in the display after typically 25 to 50 seconds of nonuse. The previously displayed value is easily retrieved without interfering with pending operations. The TI-30 turns itself off completely after typically 7 to 14 minutes of nonuse. You will never waste a battery by forgetting to turn your calculator off or by having it turned on accidentally. These features can increase the life of each battery you buy up to 50%. * Algebraic method of entry allows you to enter mathematical sequences in the same order that they are algebraically stated. + Disposable battery power source provides independence trom AC power supplies. You can always take weeks of computing power with you wherever you g0 by simply carrying a few spare batteries. * Easily convertible to a rechargeable power source. + 48 Calculator Functions Arithmetic Pethatind 4 Data Entry +l- 8 2 Display Scientific Notation 4 Scientific Notation Removal Exponent increment Exponent Decrement Algebraic x, Vx, 1x VY 5 Clearing Clear and Clear dente 2 3 Data Grouping Open and close parentheses (up to 15) and full algebraic hierarchy (up to 4 pending operations) Memory Store, Recall,Sum, Exchange 4 Percent %, +%, —%, *%, = % 5 Trigonometric Sin, Cos, Tan, Sin", Cos '', Tan ', and 3 angular modes (Degrees. Radians, Grads) Logarithmic in x, log, e*, 10° 4 Constant Operates with +,—,*.+, 6 yand Vy — 48 * Automatic Clearing — when the [=] key is pressed to the calculator is prepared for the start of anew problem. + Accuracy—The internal caiculating capacity is 11 digits even though only 8 can be displayed. This feature permits 11-digit precision in calculation. The 8 digit displayed number is rounded to within +1 in the 8th digit for all functions except where noted. Battery Installation and Considerations The Ti-30 operates on a 9-volt non-rechargeable battery, which is not supplied with the calculator since its freshness cannot be ensured. An alkaline battery is recommended for your calculator. It has an operating life of approximately 20 hours. A non-alkaline battery may be used but it should be removed prior to a prolonged period of non-use or immediately after discharge to prevent possible damage to the calculator from leakage. When the battery becomes discharged, the display becomes dim or may flash or show erroneous symbols and numbers just before fading away. 3 To install a battery, insert a coin into the slot in the back of the calculator and pry off the battery cover. (see sketch) Attach the battery terminals to the connecting wires in the calculator. Position the connected battery in the compartment according to the diagram on the battery cover and snap the cover back into place. Q Optional Accessories The following optional accessories are available from your calculator dealer or from the nearest Texas instruments Service Facility or Exchange Center. Rechargeable Kits RK-1 and RK-2—These kits are available to convert your calculator from a disposable battery power source to a rechargeable source. The RK-1 kit contains the AC9131 Adapter/Charger and the BP-5 battery pack which will typically provide 2 hours of continuous operation without recharging. About 4 hours of recharging will restore full charge when the calculator is off, 12 hours if the calculator is in use, The RK-2 kit contains the AC9132 Adapter/Charger and the BP-8 battery pack which will typically provide 4 hours of continuous operation without recharging. About 4 hours of recharging will restore full charge when the calculator is off, 6 hours if the calculator is in use. Either battery pack can be charged while in or out of the calculator. CAUTION: The battery packs cannot be recharged by either charger. The BP-5 should only be recharged with the AC9131 and the BP-8 should only be recharged with the AC9132 Carrying Case — Available at your dealer or trom Texas Instruments. 4 ll. KEY DEFINITIONS AND INDEX AE On/Clear Key — initially this key applies power to the calculator. Once the calculator is turned on, pressing this key clears an entry if no function or operation key has been pressed. When pressed after an operation or a function, this key clears the display. all pending operations and the constant. Pressing this key twice at any time clears the display, all pending operations and the constant. (GFF) Off Key — Removes power from the calculator. [0] through [9] Digit Keys — Enter numbers 0 through 9. See page 9. (=) Decimal Point Key — Enters a decimal point. See page 9. [24] Change Sign Key — When pressed after number entry or a caiculation, changes the sign of the number. The sign of the exponent is changed when this key is pressed after the [EEi) key. See page 9. (C=) Pi Key —Enters the vaiue of pi correct to 11 digits. (This value is rounded to 8 digits for display only). See page 9. [4] Add Key —Completes any previously entered arithmetic, y* or Wy function and instructs the calculator to add the next entered quantity to the displayed number. See page 15. (E) Subtract Key — Completes any previously entered arithmetic, y* or ¥’y function and instructs the calculator to subtract the next entered quantity from the displayed number. See page 15. [] Multiply Key — Completes any previously entered divide or multiply, y‘ or Wy function and instructs the calculator to multiply the displayed number by the next entered quantity. This displayed value must be less than 1 x 10” or an error condition may result. See page 15. (4) Divide Key — Completes any previously entered divide or multiply, y* or Wy function and instructs the calculator to divide the displayed number by the next entered quantity. See page 15. (=) Equais Key — Combines ail previously entered numbers and operations. This key is used to obtain both intermediate and final results. See page 15. 6 (iC) Constant Key —Stores a number and its associated operation for repetitive calculations. Enter the number, then the operation, then press [K_]. See page 23. CT)01) Parentheses Keys — Used to isolate Particular numerical expressions for separate mathematical interpretation. See page 20. (Z2] y to the x Power Key — Raises the displayed value y to the xth power. Order of entry is y [J*] x. y cannot be negative, but both x and y can be fractional. See page 26. (NY) [¥*) (= WY)x Root of y Key —Takes the xth root of the displayed vaiue y. Order of entry is y [iwv} [¥*) x. y Cannot be negative, but both x and y can be fractional. See page 26. (24) square Key —Caiculates the square of the number in the display. See page 25. C4] Square Root Key —Caiculates the square root of the number in the display. x = 0. See page 25. [Wa] Reciprocal Key — Divides the display vaiue into 1. x 4 0, See page 27. [%) Percent Key — Converts displayed number from a Percentage to a decimal. Used with +, —, x, +, this key can perform add-on, discount and percentage calculations. See page 27. {ins Natural Logarithm Key —Caiculates the natural logarithm (base @) of the number in the display. x > 0. See page 28. [it¥} [Ina] Natural Antilogarithm (e to the x Power) Sequence — Calculates the natural antilogarithm of the number in the display (raises ¢ to the displayed power). See page 28. (le) Common Logarithm Key — Calculates the common logarithm (base 10) of the number in the dispiay. x > 0. See page 29. [itv] [108] Common Antilogarithm (10 to the x Power) Sequence — Calculates the common antilogarithm of the displayed value (raises 10 to the displayed power). See page 29. DRG Degree, Radian, Grad Key — Selects the units for angular measurement. Can be changed whenever desired. See page 30. 6 [Sin] Sine Key — instructs the calculator to find the sine of the displayed value. See page 30. (ie¥) [Sin] Arcsine (sin *) Sequence — Calculates the smallest angle whose sine is in the display (first or fourth quadrant). See page 31. {ces} Cosine Key — instructs the calculator to find the cosine of the displayed value. See page 30. WV} [ces] Arccosine (cos~') Sequence — Calculates the smailest angle whose cosine is in the display (first or second quadrant). See page 31. {ian) Tangent Key — Instructs the calculator to find the po aa ny [iV] (tan) Arctangent (tan~') Sequence — Calculates Se iahee Sete whined nega a wo Wan tices ta or fourth quadrant). See page 31. {EED) Exponent Entry and Exponent/Decimai Shift Key When pressed after a keyboard entry, prepares the calculator to accept the next digits entered as the exponent (see Scientific Notation, page 10). When pressed after a result is obtained, decreases the exponent by one and moves the decimal point of the mantissa one place to the right. [Ed adds one to the exponent and moves the decimat one place to the left. See page 11, 13. S10] Store Key — Stores the displayed quantity in the without removing it from the display. Any previously stored value is cleared. See page 36. (REt] Recall Key — Retrieves stored data from the memory to the display. Use of this key does not clear the memory. See page 36. SUM Sum to Memory Key — Aigebraically adds the displayed value to the memory content. This key does not affect the displayed number or calculations in progress. See page 37. XG Exchange Key — Exchanges the content of the memory with the displayed value. The displayed value is stored and the previously stored value is displayed. See page 38. ill. BASIC OPERATIONS Your calculator is easy to operate because of its algebraic entry format which allows entry of most Problems just as they are stated. Although many ope 0 J ous, the following instruc and examples help yo skill and confidence in problem solving Turning the Calculator On Pressing MAJ. the upper right most key on the keyboard, applies power to the calculator and totally clears the calculator. Power-on condition is ind: by the presen in the display. The OFF} key. of oc e f the display is no press [OFF] to reset the ca’ e of alighted Initial Display addition to power-on and numerical information, the display provides indication of a negative numb decimal point, angular mode and error. As many as 8 digits can be entered. Ail cigit keys pressed after the 8th are ignored floating minus sign Any negative number is displayed with a minus sign immediately to the lef vuMber just as negative numbers are normaily written. The minus sign is located here instead of on the far left of the display for ease of reading 8 Automatic Turn-Off Electronic control (as opposed to switch contro!) of ON and OFF, allows the calculator to minimize power consumption by displaying a number for only a limited length of time. The display reverts to a traveling decimal point after typically 25 to 50 seconds of nonuse. As soon as any key is pressed, the display is restored. The safest method of reactivating the display is to press [EXC] twice. This insures that calculations in progress are not affected and that processing continues as though nothing had happened to the display. The benefit is a substantial increase in the operating life of your battery. If not interrupted, the traveling decimal display continues for a period of 7 to 14 minutes then automatically turns the caiculator completely off. Data Entry For maximum versatility, your calculator operates with a floating decimal point. When entering numbers. the decimal remains to the right of the mantissa until [+ ] is pressed. Then the fractional part of the number is onl ee casa lsstaabn (@ through (H) Digit Keys — Enter numbers 0 through 9. [=] Decimal Point Key — Enters a decimal point. [54 Crange Sign Key — When pressed after number entry or acaiculation, changes the sign of the displayed number. The sign of the exponent is changed when this key is pressed after the (EE) key. (=) Pi Key—Enters the vaiue of pi correct to 11 digits. (This value is rounded to 8 digits for display.) Numbers up to 8 digits in length can be entered into the calculator directly from the keyboard. The calculator can hold and work with 11 digits. Numbers of this length can be entered as the sum of two numbers. Example: Enter 389182.70636 Enter Pr Display 389182 389 182 -70636 3) 389 182.71 Clearing To remove an incorrect entry from the display before any function or operation key is used, press When pressed after an operation or function key (including &) ), this key clears the display, the constant and all pending operations. Pressing PWG twice always clears the dispiay, the constant and pending operations. The memory is not affected by this key. Scientific Notation To enter very large or very small numbers you must use scientific notation where the number is entered as a number (mantissa) multiplied by 10 raised to some power (exponent) such as ~ 3.6089 x 10”, mantissa exponent 1 1 wt integer decimal exponent sign floating minus sign The entry procedure is to key in the mantissa (including its sign), then press (EE) and enter the power of ten. Any number smaiier than +1 = 10-* or larger than 499999999 must be entered in scientific notation. The number 320,000,000,000 can be written 3.2 « 10" and can be entered into the calculator as: Enter Press Display 0. 3.2 ~ (ea 3.2 00 " 3211 The last two digits on the right side of the display are used to indicate the exponent of 10. Additional digits can be entered after pressing [E£i), but only the last two numbers pressed are retained as the exponent. In scientific notation, a positive exponent indicates how many places the decimal point should be shifted to the right. If the exponent is negative, the decimal should be moved to the left. of how a mantissa is entered in scientific notation, the calculator normalizes the number, displaying a single digit to the left of the decimal point. when any function or operation key is pressed. Exampie: Enter 6025 x 10” Enter Press Display ws 0. 6025 (ee) 6025. 00 20 6025. 20 wm 6.025 23 The decimal point of the entered mantissa must not be beyond the Sth digit from the left because the mantissa for scientific notation is limited to § digits in the display. Eight can be entered, but only 5 are displayed when is pressed. The entire eight digit mantissa is used for calculations. The display does not go into scientific notation format if more than S numbers are entered to the left of the decimal point. "W The change sign key can be used to attach a negative sign to the mantissa and to the power-of-ten exponent. Example: Enter -4.818 x 10°? Enter Press Display bud 0. 4818 tras] 4.818 00 10 leas] 4818-10 Acaiculated result or quantity recalled from memory only, to convert a result in standard format to scientific notation press [X] 1 (£0) (=). Example: 89 x 987 = 87843 = 8.7843 « 10° Enter Press Display 89 oo 89. 987 & 87843. ie 8) 87843. 1 (ey 1. 00 | 8.7843 04 Data in scientific notation form may be entered intermixed with data in standard form. The calculator converts the entered data for proper calculation. Example: 3.2 x 10 + 12575.321 = 15775.321 Enter Press Display om 0. 3.2 3.2 00 3 2 3.2 03 12575.321 3) 5-3) 1.5775 04 1 (iy) (ed (=) 18775.321 Notice that the complete answer to the probiem is 15775.321 and this is the number used for further calculations. Actually, the calculator internally carries ail intermediate caiculations and final results to 11 places. These numbers are rounded to a maximum + iibntoatia phat aaah 12 This example also shows how the display can be removed from scientific notation format. The displayed number must be in the range +1 = 10°* to+1 = 10%. After a number entry, press then an operation key or equals to produce a result in standard display format. Once in scientific notation, the calculator will remain in scientific notation format until BAY is pressed or the above procedure performed. Exponential Shift ET] key can be used to alter the appearance of the displayed number without changing its value. When this key is pressed after a result is obtained or after a function or operation key is pressed, it decreases the exponent by one and moves the decimal point of the mantissa one place to the right. [iw] (EEN) adds one to the exponent and moves the decimal one place to the left under the same conditions. Example: 1.2 x 10 + 3.45 x 10" = 1.2345 x 10 = 12.345 x 10" = 1.2345 x 10" Enter Press Display 12 1,2 00 16 1.2 16 3.45 3.45 00 “4 1.2345 16 12.345 15 wv) (EES) 1.2345 16 Practical Example: What is the diameter of a cable, in microns (1 micron = 10°* meter), whose circumference is 3x 10°? meters? C= wd, d= C/n. (ee) 3) (ey) & Enter Press Display 3 3. 00 3 fa) 3-03 wae 9.5493-04 . (eed) 95.493 -05 (ee) 954.93-06 The diameter is 954.93 microns. 13 When increasing the magnitude of the mantissa, you cannot shift past a §-digit integer. When decreasing the mantissa, zeros can be added between the decimal Point and the number, possibly pushing some digits out of the display. Once digits have been shifted out of the display, they cannot be returned to the display by the shifting process. Internally, the number is always retained to its full unshifted value. The normalized display is returned whenever any operation, special function, memory or equal key is pressed. To restore Ce re rene CRETE, reer twice. Error Indication The display shows “Error” whenever overfiow or underflow occurs or when an improper mathematical operation is requested. When this occurs. any from the keyboard is not accepted until fiw or is pressed. This clears the error condition and ail pending operations. You must now return to the first of your problem and begin again. The error message is given for the following reasons. 1. Number entry or calculation result (including summation into memory) outside the range of the calculator, +1.0 x 10°” to+9.9999 « 10”. 2. Dividing a number by zero. 3. The mantissa is zero and (1a), [Inx} or (Valis pressed. 4. The mantissa is negative and (eg), (7=).[¥*). [ina] or (iV) [7] is pressed. 5. Inverse of sine or cosine (arcsine, arccosine) when the mantissa is greater than 1. 6. Tangent of 90", 270", 100 grads, 300 grads or their rotation multiples like 450°, etc. 7. Having more than 15 open levels of parentheses with each pending operation or more than four pending operations. * 8. Multiplying a number greater than the 1 x 10” by another number (decimal or integer) may cause an error condition. 14 IV. ARITHMETIC FUNCTIONS System. sequences to be interpreted correctly by storing certain quantities and operations until the algebraic principles say they can be completed. A more complete discussion of this system occurs later in this section. itis a sate procedure to press the Bi¥G key before the start of each new problem. This process is not required when the previous problem used [=] to obtain the final result. Following [=] with a numeric entry automatically clears the previous result. Example: 23.79 + 54-6 = 1833 Enter Press Display : 0. 23.79 <3} 23.79 ss ia] 24.33 6 3] 18.33 Again note that the numbers and functions are entered in the same order as they are mathematically stated. Example: ~3.7 — (-7.09) + .014 = 3.404 Enter Press Display 37 moe -37 7.09 <3] 3.39 O14 3) 3.404 Example: -4 «7.3 + 2=-146 Enter Press Display 4 FAL) 4. 73 3] -292 2 & -46 6 Input Error Correction At any point in a calculation, BW can be pressed twice to clear all calculations, including any errors and start over. This drastic action is seldom necessary. if an incorrect number entry is made, pressing the key before any non-number key clears the incorrect number without affecting any calculation in progress. Special circuitry has been provided to facilitate the correction of a wrong operation entered while keying in your problem. When there are no stored operations. as when the first operation is keyed in, and an unwanted operation key is entered, simply press the correct and continue. This applies to[ +], [=] Neale) and (iv) (7). Correction of an incorrect operation entry while there are stored operations in the calculator is dependent on the table below. INCORRECT DESIRED ENTRY ENTRY i +- | wy y¥ vy = did CK" | ON/C | ON/C | ON/C y cK cK ON/C vy cx | ot ck “CK means to press the correct key and continue. Locate the incorrect entry you have just made in the column on the left, then follow that row over to the desired operation and apply whatever instruction occurs at that junction. 16 The SM key in the table indicates that the incorrect entry cannot safely be corrected to the desired operation for all conditions so the problem must be restarted. Example: 64x 74 + $3 = 45 Enter Press Display Comments 6 moo «6 First operation wrong 7 Be 4 6 x 7 Completed 4 0. Clears 4 (entry) 3 & 45. Answer A full understanding of the calculator hierarchy discussed in the next few pages will make the input error correction methods obvious, Combining Operations After a result is obtained in one calculation it may be directly used as the first number inasecond calculation. There is no need to reenter the number from the keyboard. Example: 1.84 + 0.39 = 2.23 then (1.84 + 0.99)/365 = 00610959 Enter Press Display Comments 1.84 3] 184 39 & 2.23 1,84 + 0.39 ic) 2.23 3} .006 10959 2.23+ 365 v7 Calculator Hierarchy In order to efficiently combine operations. you need to understand the standard algebraic rules that have been specifically programmed into the calculator. These algebraic rules assign priorities to the various mathematical operations. Without a fixed set of rules, expressions such as 5 x 4 + 3 x 2 could have several meanings: Sx (4+3)x 2=70 or5x4+3x2= 26 or(5 x 4+3)x 2=46 or5 x (4+3x 2)=50 Algebraic rules state that multiplication is to be performed before addition. So, aigebraicly, the correct answer is (5 x 4) + (3 x 2) = 26. The complete list of Priorities for interpreting expressions is: 1) Singie-variable Functions 2) Exponentiation (y*), Roots (Vy) 3) Multiplication, Division 4) Addition, Subtraction 5) Equals 2) Exponentiation (y*) and roots (Vy) are performed a3 soon as the single-variabie functions are completed. 3) Multiplication and division are performed as 800N as the special functions, exponentiation, root extraction and other multiplication and division are completed. 4) Addition and subtraction are performed only after all operations through multiplication and division as well as other addition and subtraction are completed. 5) Equats completes all operations. 8 To illustrate, consider the interpretative order of the following example. Example: 4+ 5 x 7+ 3 * 5" = 3.2413203 Enter Press Display Comments 4 4. (4+) is stored 5 25. cig (5?) single-variabie function [x#] evaluated immediately 0.16 (4+ 5*) evaluated because x is same priority as +. 1.12 x higher priority than + 80 (4+ 5 x 7) evaluated, + stored . (3%) stored. 05 .Sy' stored 0.5 Cos 60° evaluated immediately. 3.2413203 Completes all operations: 5°" evaluated, then 3 x 5°" next, then this is added to 1.12. Thus. by entering the expression just as it is written, the calculator correctly interprets it. The important thing to remember here is that operations are enacted strictly according to their relative priority as stated in the rules. The calculator remembers all stored operations and recalls each and its associated number for execution at exactly the correct time and place. Once familiar with the order of these operations. you will find most problems are extremely easy to solve because of the straightforward manner in which they can be entered into the calculator. When parentheses are required to properly write an equation. parentheses are aiso available on the calculator. In the expressions at the top of page 18, the parentheses entered, as shown, will result in the answers shown. © OER BH Parentheses There are sequences of operations for which you must instruct the calculator exactly how to evaluate the 4x (G+ He (7-477 +427? © To evaluate this expression as written using only the calculator hierarchy, many independent steps would be required. Also, intermediate results would have to be stored and the sequence certainly could not be input in the same order in which it is written. Parentheses should be used here and whenever a mathematical Sequence cannot be directly entered using the previously mentioned algebraic rules or when there is doubt in your mind as to how the calculator is going to reduce an expression. To illustrate the benefit of parentheses. try the following experiment: press (C] 5 (+9) J. and you will see the value 14 displayed. The caiculator has evaluated 5 + 9 and replaced it with 14 even though the [=] key was not pressed. Because of this function of parentheses, the algebraic rules now apply their hierarchy of operations within each set of parentheses. Use of parentheses insures that your problem can be keyed in just as you have written it down. The calculator remembers each operation and evaluates each part of the expression as soon as all necessary information is available. When a closed parenthesis is encountered, ail operations included within the parenthesis pair are completed. Parentheses have the additional capability of supplying a missing operand, as shown by the following example. Example: 4 - (4 + 2) = -2 Enter Press Display 4 GIO 4 2 oH 6. = -2 if no value is entered after a ( . the calculator uses the value in the display register. in the example a 4 was automatically inserted before the +. 20 Aclosed operand. For instance, Forman, C21 Ci anen®.the sel Lge the display value 3 for the missing operand. Example: 4 = (5 + 9) + (7 ~- = aye 1 = 29005288 Key in this expression and follow the path to completion. Enter Press Display Comments 4 oc 4. (4x) stored pending evaluation of parentneses: 5. (5+) stored 14. (5 + 9) evaluated 56. Hierarchy evaluates 4x4 56. pach ered is 2) ow ic) co evaluation of parentheses 7 oo 7. (7-) stored 4 oO 3. (7-4) evaluated fm 3., Prepares for exponent 2 | 2. 3 oOo S. (2+ 3) evaluated e .23045268 (7 — 4)? * * evaluated then divided into 4x(5+9) There are limits on how many operations and associated numbers can be stored. Actually, as many as fifteen parentheses can be open at any one time and four operations can be pending. but only in the most complex situations would these limits be approached. One or more leading parentheses shift Sore ot processing w the second level showing for only 3 pending operations. If you do attempt to open more than 15 parentheses or if the calculator tries to store more than four operations, the error message appears in the display. * The following example, requiring the storage of 4 operations, shows the order of interpretation provided by the caiculator's operating system. 21 Example: 5 + (8/(9 — (2/3))) = 5.96 Enter Press Display Comments 5 mo 5. (5+) stored 8 Bo 8. (8+) stored 9 G1CO 9 (9-) stored 2 ie] 2. (2+) stored 3 oo 66666667 (2/3) evaluated oI 8.3333333 (9 ~ (2/3) evaiuated oI 0.96 (8/(9 — (2/3))) 3] » see 5 + (8/(9 - (2/3) Because the [=] key has the capability to complete all incomplete operations whenever it is used. it could have been used here instead of the three [_)_] keys. Try again and pressi instead priya nots) Each time a closed parenthesis is encountered, the contents are evaluated back to the nearest open parenthesis and are replaced with asinglevaiue. Knowing this you can structure the order of interpretation for whatever purpose you may want. Specifically, you can check intermediate results. Example: 3 x (42°) = 47000434 Enter Press Display Comments 0. 3 COCO 3. 4 iE dod § 4 2 16 od | 8} sx 7 iw) 7. 4 oI 1.6265766 Ww itv] —1.6265766 = -(W7) om 32385579 2-(7) ol 15666811 4" & 4.7000434 3x 4™.-- Note that in ail these examples. the expressions are entered in a straight left to right sequence. 22 Calculations With a Constant Repetitive calculations have been simplified through use of the constant feature of the calculator. Entry of arecurring sequence such as +3, « (-17.3) ory’ canbe stored and used by the calculator to operate on any displayed number. To use the constant feature, enter the repetitive number, m, then enter the desired operation, then press [K ]. m(+](K) adds mtoeach subsequent entry. oI) subtracts m from each subsequent entry. m(X](K] _ multipties each subsequent entry bym. a) 00 divides each subsequent entry by m. m(¥*) (KI raises each subsequent entry to the m power. m [INV] [7*] [i] takes the m™ root of each subsequent entry. After storing the constant, each calculation is completed by entering the new number and pressing [=]. Clearing the calculator or entering any of the above arithmetic functions eliminates the constant that is currently stored. : Example: 31+ 1.8026 = 32.8026 745.797 + 1.8026 = 747.5996 8.002 + 1.8026 = -6.1994 3.2 10? + 1.8026 = 18346 Enter Press Display owe 0. 1.8026 Boo 1.8026 un 3} 32.8026 745.797 3) 747.5996 8.002 wae 6.1994 32 (fé) 3.2 00 2 (=) 1.8346 00 Example: Evaluate (3.75)-*#, (.1066)">, (.0692)-** Enter Press Display 3.2 G00 -32 a7) 01455794 06s = (=) 1291.7455 eo2 [=] $148.2603 Accuracy and Rounding Each calculation produces an 11-digit result, These 11 digits are more than are displayed. The result is therefore rounded to a 8-digit standard display or toS digits for scientific notation. The 5/4 rounding technique built into this calculator adds 1 to the least significant digit of the display if the next, non-displayed digit is five or more. If this digit is less than five, no rounding is applied. in the absence of these extra digits, inaccurate results would frequently be displayed, such as VW/3 x 3= 99999999 The example shows 1+ 3.= .33333333 when multiplied by 3 produces this answer. The internal 11-digitstring of nines in your calculator is rounded to 1. The higher order mathematical functions use iterative calculations. The cumulative error from these calculations in most cases is maintained beyond the eight-digit display so that no inaccuracy is displayed. Most calculations are accurate to +1 in the eighth digit as long as the calculator is not in scientific notation. The only exceptions are the tangent function as it approaches undefined limits and y* where y is within 10°° of 1 a4 V. SPECIAL FUNCTIONS The special function keys described in this section are singie-variable functions except for y* and ¥’y which are two-variable functions. The single-variable functions operate only on the displayed value without interfering with calculations in progress. The two- variable functions may be isolated within a calculation by parenthesis or used with the calculator hierarchy. NOTE: The right-most digit is displayed during the short time the calculator is computing a result. Be sure the calculator has completed an operation before pressing the next key. Roots and Powers The square key [##) calculates the square of the number x in the display. Example: (4.235) = 17.935225 Enter Press Display 4.235 17.935225 The square root key [% ] calculates the square root of the number x in the display. Example: V625 = 25 Enter Press Display 6.25 (2) 25 Example: (V3. 1452 — 7 + (3.2)'1"? = 2.2390782 Enter Press Display 3.1452 fie) 1.77347 12 7 @ ~$.2265288 3.2 Le] 10.24 3 $.0134712 cca] 2.2390782 Your calculator also provides two universal roots and powers keys that allow you to vary the value of the exponent as well as the value of the base. One is accessed by the [¥®] key. The other is accessed by the IN key sequence providing Wy. These functions are the only special functions that do not act on the two keys is identical. Enter y, press [¥*] or [inv] (¥*] enter x, and press [=] or an arithmetic function key to yield the answer. A closed parenthesis also completes these functions as well as other stored operations back to the nearest open parenthesis. Example: 2.86-? = 64317072 Enter Press Display 2.86 62] 2.66 42 ~0.42 & 64317072 Example: 7/1460 = 10.332744 Enter Press Display 1460 ) “4460. . 3.12 & 10.332744 There is a restriction on these functions — the variable y must be non-negative. When y is negative “Error” lights up in the display after x and an operation key are pressed. y cannot be negative because logarithms are used to perform these functions. The Oth root of a number is not a natural mathematical operation and consequently results in an error condition. Any non- Negative number taken to the zero power is 1. Accuracy for these roots and powers is within +1 in the 8th significant digit over all ranges except for values of y very near 1 and very large exponents or very small roots. For example 1.00008**" has an error of 4 in the 6th digit. These errors increase as y approaches 1and the exponent becomes extremely large or when roots become extremely small. Reciprocal ee ee ee cee 1x0. Example: 41, = 0.3125 Enter Press Display 32 (Vi) 0.3125 Example: — = 58129595 nes oe Enter Press Display Comments 1 @ 1. Enter -1 74 cca 1.7202941 -14.VT4 [Vz] 58129595 Answer Percent The percent key converts the displayed number from a percentage to a decimal. Example: 43.9% = 439 Enter Press Display 439 3] 0.439 When [%] is pressed after an arithmetic operation, add on, discount, and percentage can be computed as fotiows; [¥] n[%] [=] adds n% to the number displayed. Example: What is the total cost of a $15 item when there is a 5% sales tax? Enter Press Display 1s 3] 1s ’ ae 15.75 (219 (¥) (=) subtracts n% from the number L Example: How much is paid for a $5 item that has been discounted 2%? Enter Press Display 5 i) 8. 2 me) 49 (32) n [X) [=] muttipties the number in the display by n%. Example: What is 25% of 15? Enter Press Display 16 bo 15. 25 ae 0.375 CE) n (3) (=) divides the displayed number by n%. Example: 25 is 15% of what number? Enter Press Display 25 & 25. 1s We 166 66667 Natural Logarithm and e* The natural logarithm key [ing] caiculates the natural logarithm (base e) of the number x in the display. x>0. Example: in 1.2 = 16232156 Enter Press Display 12 {in} -18232156 The natural antilogarithm (e to the x power) sequence [lev] (inz} calculates the natural antilogarithm of the number in the display. ico aa begadaia Example: e?" = 45.150439 Enter Press Display 3.81 (ONY) (ine) 45. 150439 Example: @7**!'+" = 2531.2594 Enter Press Display Comments wo 0. 7s <3] 758 Enter 7.5 14 133647224 int4 A 7.8364722 (7.5+1n 1.4) Note that the [=] key is not needed as the special function produces the final result. Common Logarithm and 10° The common logarithm key [Tg] calculates the common logarithm (base 10) of the number x in the display. x > 0. Example: log 32.01 = 1.5052857 Enter Press Display 32.01 15052857 The common antilogarithm (10 to the x power) sequence [iN¥} calculates the common ant of the value. This sequence raises 10 to the displayed power. Example; 10°’"* = 7.5858 x 10° Enter Press Display 7.12 7,$858-08 Example; log (303 + 10") = 2.510959 Enter Press Display Comments omg 0. 303 ic) 303. Enter 303 1360 (i) 22.908677 10°" ow 325.90868 303+ 10°" (ies) 25130959 Answer The results from logarithms (natural and common), when displayed in normal form rather than in scientific notation, are accurate within the displayed digits. Trigonometric Functions The degree, radian, grad key DRG selects the units for angular measurement. When the calculator is first turned on, it is in the degree mode. Pressing the PRG key once places the caiculator in the radian mode. Press this key again and your angles are measured in grads (right angle = 100 grads). The mode changes in 4 rotary fashion each time the key is pushéd. Another key push, for instance, returns the calculator to the degree mode. The display indicates the current angular mode of the calculator. An apostrophe (’) in the far left side of the display denotes the radian mode while quote marks (") indicate the grad mode. If the apostrophe and quotes are absent, angles are measured in degrees. The angular mode has absolutely no effect on calculations unless the trigonometric functions are being used. Selecting the angular mode is an easy step to perform —and to forget! Neglecting this step is responsible for a large portion of errors in operating any calculating machine that offers a choice of angular units. When the trig functions (sine, cosine, and tangent) are activated, they compute their respective functions of the angie in the display. The inverse trig functions find the smaliest angle whose function vaive is in the display. are accurate for any degrees < 3.6 = 10",-200 r to 200 © radians and —40,000 to 40,000 grads. in general, the accuracy decreases one digit for each decade outside this range. Example: sin 30° = 0.5 = sin 390° Select degree mode Enter Press Display 30 [sia] Os 390 (sia) Os Example: [sin (.3012 w)}-*"** = 1.0626654 Select radian mode (') Enter Press Display oa) : 0. 3012 [X) " 0.3012 (e) '3.1415927 oO "94624771 "91122714 i de] "81122714 16.2 Comments (3012 ») Sin (.9012 ») Tan 16.2" Answer The largest angle resulting from an arc function is 180 degrees (7 radians or 200 grads). Because certain angles have identical function values within one revolution, i.e., arcsin = .S for 30° and 150", the angle returned by each function is restricted as follows: Arc Function Quadrant of Resultant Angie arcsin x (sin-' x) First (0 to 90", r/2, or 100 G) arcsin -x(sin"'-x) Fourth (0 to-90", —#/2, or —100 G) arccos x (cos™* x) First (0 to 90°, /2, or 100 G) arccos — x (cos~'-x) Second (90° to 180°, 7/2 tom, or 100 to 200 G) arctan x (tan"' x) First (0 to 90", #/2, or 100 G) arctan —x(tan-'-x) Fourth (0 to -90°, —#/2, or —100 G) Arcsin .5, for example, always returns 30? as the angie even though sin 150° = .5, sin 390° = .5, etc. as well, - Exampie: sin~' .712 = 45.397875 degrees - .79234239 radians Select degree mode Enter Press Display 712 (eev) 45.397875 Select radian mode (‘) Enter Press Display 712 [in] (sin) "79234239 Example: Varetan 57 1 i+ gag = 9-1905773 degrees Select degree mode Enter Press Display Comments 9.72 (INV) [faa) $4.126039 arctan9.72 (VCE) © 91720248 -Varctan 9.72 §3.900984 @rcsin 808 01855254 Varcsin 808 9.1905773 Answer Sine and cosine functions are accurate throughout all displayed digits when displayed in standard form. The tangent of +90° or +100 grads results in an error condition because the function is undefined at these points. As the tangent approaches these undefined limits the accuracy is restricted. For example, the tangent of 89 degrees (1.5533 radians or 98.888889 grads) is accurate throughout the 8 displayed digits whereas tan 89.99999" is accurate to 3 places. Degree, Radian, Grad Conversions itis frequently necessary to convert angular valu