fx-115WA fx-991WA User’s Guide E Removing and Replacing the Calculator’s Cover • To Remove the cover Grasp the top of the cover, and slide the unit out from the bottom. • To Replace the cover Grasp the top of the cover, and slide the unit in from the bottom. Always slide the unit into the cover with the unit’s display end first. Never slide the keyboard end of the unit into the cover. CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Circular Road, London NW2 7JD, U.K. Safety Precautions Be sure to read the following safety precautions before using this calculator. Keep this manual handy for later reference. Caution This symbol is used to indicate information that can result in personal injury or material damage if ignored. Batteries • After removing the batteries from the calculator, put them in a safe place where there is no danger of them getting into the hands of small children and accidently swallowed. • Keep batteries out of the reach of small children. If accidently swallowed, consult with a physician immediately. • Never charge batteries, try to take batteries apart, or allow batteries to become shorted. Never expose batteries to direct heat or dispose of them by incineration. • Misuse of batteries can cause them to leak acid that can cause damage to nearby items and creates the possibility of fire and personal injury. • Always make sure that a battery’s positive k and negative l sides are facing correctly when you load it into the calculator. • Remove the batteries if you do not plan to use the calculator for a long time. • Use only the type of batteries specified for this calculator in this manual. Disposing of the Calculator • Never dispose of the calculator by burning it. Doing so can cause certain components to suddenly burst, creating the danger of fire and personal injury. 앫1앫 • The displays and illustrations (such as key markings) shown in this User’s Guide are for illustrative purposes only, and may differ somewhat from the actual items they represent. • The contents of this manual are subject to change without notice. • In no event shall CASIO Computer Co., Ltd. be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. Handling Precautions • Be sure to press the • • • • key before using the calculator for the first time. Even if the calculator is operating normally, replace the battery at least once every three years. Dead battery can leak, causing damage to and malfunction of the calculator. Never leave the dead battery in the calculator. The battery that comes with this unit discharges slightly during shipment and storage. Because of this, it may require replacement sooner than the normal expected battery life. Low battery power can cause memory contents to become corrupted or lost completely. Always keep written records of all important data. Avoid use and storage in areas subjected to temperature extremes. Very low temperatures can cause slow display response, total failure of the display, and shortening of battery life. Also avoid leaving the calculator in direct sunlight, near a window, near a heater or anywhere else it might become exposed to very high temperatures. Heat can cause discoloration or deformation of the calculator’s case, and damage to internal circuitry. 앫2앫 • Avoid use and storage in areas subjected to large • • • • • amounts of humidity and dust. Take care never to leave the calculator where it might be splashed by water or exposed to large amounts of humidity or dust. Such elements can damage internal circuitry. Never drop the calculator or otherwise subject it to strong impact. Never twist or bend the calculator. Avoid carrying the calculator in the pocket of your trousers or other tight-fitting clothing where it might be subjected to twisting or bending. Never try to take the calculator apart. Never press the keys of the calculator with a ball-point pen or other pointed object. Use a soft, dry cloth to clean the exterior of the unit. If the calculator becomes very dirty, wipe it off with a cloth moistened in a weak solution of water and a mild neutral household detergent. Wring out all excess moisture before wiping the calculator. Never use thinner, benzine or other volatile agents to clean the calculator. Doing so can remove printed markings and damage the case. 앫3앫 Contents Safety Precautions ........................................... 1 Handling Precautions ...................................... 2 Two-line Display ............................................... 5 Key Layout ........................................................ 6 Before Starting Calculations... ...................... 7 kModes .................................................................... kInput Capacity ........................................................ kMaking Corrections During Input ........................... kReplay Function ..................................................... kError Locator .......................................................... kExponential Display Formats ................................. kAnswer Memory ..................................................... 7 8 8 8 9 9 9 Basic Calculations ......................................... 10 Memory Calculations ..................................... 10 kIndependent Memory ........................................... 10 kVariables .............................................................. 10 Fraction Calculations .................................... 11 kFraction Calculations ............................................ 11 kDecimal-to-Fraction Conversion ........................... 11 kFraction-to-Decimal Conversion ........................... 11 Percentage Calculations ............................... 12 Scientific Function Calculations .................. 13 kTrigonometric/Inverse Trigonometric Functions ... 13 kHyperbolic/Inverse Hyperbolic Functions ............ 13 kAngle Unit Conversion ......................................... 14 kCommon and Natural Logarithms/ Antilogarithms ...................................................... 14 kSquare Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals, Factorials, Random Numbers and π .......................................... 14 kFIX, SCI, RND ..................................................... 15 kENG Calculations ................................................ 16 kInputting ENG Calculation Symbols ..................... 16 kCoordinate Conversion (Pol(x, y), Rec (r, θ )) ............ 17 kPermutation ......................................................... 18 kCombination ......................................................... 18 앫4앫 Statistical Calculations .................................. 18 kStandard Deviation (SD Mode) ............................ 18 kProbability Distribution Calculations ................... 19 kRegression Calculations (REG Mode) ................. 20 Complex Number Calculations (CMPLX Mode) ................................................ 22 kAbsolute Value/Argument Calculation ................. 23 Metric Conversions ( fx-991WA ) ................... 23 Scientific Constants ( fx-991WA ) .................. 25 Base-n Calculations ....................................... 26 Degrees, Minutes, Seconds Calculations .... 28 Technical Information .................................... 28 kWhen you have a problem...... ............................. kError Messages ................................................... kOrder of Operations ............................................. kStacks .................................................................. kPower Supply ...................................................... kInput Ranges ....................................................... 28 29 30 31 31 33 Specifications ................................................. 35 Two-line Display You can simultaneously check the calculation formula and its answer. The first line displays the calculation formula. The second line displays the answer. 앫5앫 Key Layout Layout Key < fx-991WA > Page Page Page Page 17 Rec( 25 11 17 14 28 15 14 27 DEC HEX 10 BIN 15 10 16 10 11 28 10 14 10 C B 10 19 28 23 DISTR 13 20 23 Re<->lm 10 20 16 M 20 16 arg e OCT 14 13 10 14 13 10 cos-1 E tan-1 F 13 23 10 13 19 10 10 10 Abs X M- Y 19 M DT CL 8 10 10 18 T INS McI ScI 20 16 20 16 8 18 18 m k nPr nCr 18 16 18 16 20 20 14 12 B G µ 18 16 r 14 14 27 sin-1 D 10 10 10 20 16 20 16 f Page 15 24 CONV y Page ON/CLEAR x! LOGIC A Page Page MODE 15 27 A Page Page 2 REPLAY ALPHA Page 15 Page 17 23 Page Page 8 11 SHIFT C p 15 15 Rnd Ran# Page CONV n 15 DRG 10 18 9 nPr nPr 18 nCr fx-115WA: 앫6앫 y 19 Before Starting Calculations... k Modes Application Mode Name Mode Indicator COMP – CMPLX CMPLX SD SD Calculation Modes Normal calculations Complex number calculations Standard deviation calculations Regression calculations Base-n calculations REG REG BASE-N b (binary) o (octal) d (decimal) H (hexadecimal) Angle Unit Modes Degrees Radians GRA R T B NORM1 NORM2 – – FIX Fix SCI Sci ENG ENG DEG RAD Grads Display Modes Exponential notation (Canceling FIX and SCI specification) Number of decimal place specification Number of significant digit specification Exponential display range specifications Note! • Mode indicators appear in the lower part of the display, except for the Base- n indicators which appear in the exponent part of the display. • The ENG mode cannot be selected while the calculator is in the CMPLX or BASE-N mode. 앫7앫 • You cannot set the angle unit or the display mode while the calculator is in the BASE-N mode. • The COMP, CMPLX, SD, and REG modes can be used in combination with the angle unit modes. • Be sure to check the current calculation mode (SD, REG, COMP, CMPLX) and angle unit mode (DEG, RAD, GRA) before beginning a calculation. k Input Capacity • The memory area used for calculation input can hold 79 “steps.” Whenever you input the 73rd step of any calculation, the cursor changes from “_” to “k” to let you know memory is running low. If you still need to input more, you should divide your calculation into two or more parts. k Making Corrections During Input • Use e and r to move the cursor to the location you want. • Press [ to delete the number or function at the current cursor position. • Press A K to change to an insert cursor t . Inputting something while the insert cursor is on the display inserts the input at the insert cursor position. • Press e, r, A K, or = returns to the normal cursor from the insert cursor. k Replay Function • Pressing r or e recalls the last calculation you performed. You can then make any changes you want in the calculation and re-execute it. • Pressing t does not clear Replay memory, so you can recall the last calculation even after you press t. • Replay memory is cleared whenever you start a new calculation, change to another mode, or turn off power. 앫8앫 k Error Locator • Pressing r or e after an error occurs displays the calculation with the cursor positioned at the location where the error occurred. k Exponential Display Formats This calculator can display up to 10 digits. Larger values are automatically displayed using exponential notation. In the case of decimal values, you can select between two formats that determine at what point exponential notation is used. Press F F F F 3 1 (or 2) to select NORM 1 or NORM 2. • NORM 1 With NORM 1, exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than two decimal places. • NORM 2 With NORM 2, exponential notation is automatically used for integer values with more than 10 digits and decimal values with more than nine decimal places. • All of the examples in this manual show calculation results using the NORM 1 format. k Answer Memory • Whenever you press = after inputting values or an expression, the calculated result is automatically stored in Answer Memory. You can recall Answer Memory contents by pressing g. • Answer Memory can store up to 12 digits for the mantissa and two digits for the exponent. • Answer Memory contents are not changed if the operation performed by any of the above key operations results in an error. 앫9앫 Basic Calculations • Use the COMP mode for basic calculations. • Example 1 : 3(510–9) 3-R 5eD 9T= 1.5-08 • Example 2 : 5(97) 5-R 9+7 T= 80.00 • You can skip all T operations before =. Memory Calculations k Independent Memory • Values can be input directly into memory, added to memor y, or subtracted from memory. Independent memory is convenient for calculating cumulative totals. • Independent memory uses the same memory area as variable M. • To clear independent memory (M), input 0 j 3. • Example: 23 9 32 53 6 47 ) 45 2 90 (Total) –11 23 + 9 j 3 32.00 53 , 6 | 47.00 45 - 2 A { 90.00 03 –11.00 k Variables • There are nine variables (A through F, M, X and Y), which can be used to store data, constants, results, and other values. • Use the following operation to delete data assigned to all nine variables: A C = . • Use the following operation to delete data assigned to a particular variable: 0 j 1 . This operation deletes the data assigned to variable A. 앫10앫 • Example: 193.2 23 8.4 193.2 28 6.9 193.2 j 1 \ 23 = 8.400 p 1 \ 28 = 6.900 Fraction Calculations k Fraction Calculations • Use the COMP mode for fraction calculations. • Values are automatically displayed in decimal format whenever the total number of digits of a fractional value (integer numerator denominator separator marks) exceeds 10. • Example 1 : 2 4 1 3 5 2C3 +1C 4C 5= 2 7 15.00 1 1.6 2 1 C 2 + 1.6 = 2.100 • Example 2 : • Fraction/decimal calculation results are always decimal. k Decimal-to-Fraction Conversion • Example: 2.75 → 2 3 4 2.75 = 2.75 C 2 3 4.00 AB 11 4.00 k Fraction-to-Decimal Conversion • Example: 1 ↔ 0.5 (Fraction ↔Decimal) 2 1C 2= 앫11앫 1 2. 00 C 0.500 C 1 2. 00 Percentage Calculations • Use the COMP mode for percentage calculations. • Example 1 : To calculate 12% of 1500 1500 - 12 A v 180.00 • Example 2 : To calculate what percentage of 880 is 660 660 \ 880 A v 75.00 • Example 3 : To add 15% onto 2500 2500 - 15 A v + 2875.00 • Example 4 : To discount 3500 by 25% 3500 - 25 A v , 2625.00 • Example 5: If 300 grams are added to a test sample originally weighing 500 grams, what is the percentage increase in weight? 300 500 100 160 (%) 500 300 + 500 A v 160.00 • Example 6: If temperature changes from 40°C to 46°C, what percentage did it rise? 46 40 100 15 (%) 40 46 , 40 A v 앫12앫 15.00 Scientific Function Calculations • Use the COMP mode for scientific function calculations. • = 3.14159265359 k Trigonometric/Inverse Trigonometric Functions • Example 1 : sin63°5241 q q q 1 →“ R ” 00 S 63 I 52 I 41 I = 0.897859012 R π rad 3 q q q 2 →“ T ” • Example 2 : cos ( ) 0.500 WRAx\3T= T 2 π rad 2 4 q q q 2 →“ T ” • Example 3 : cos1 WA V RL2\2T= 0.78539816300 g\Ax= 0.2500 T • Example 4 : tan1 0.741 q q q 1 →“ R ” A g 0.741 = 36.5384457700 R k Hyperbolic/Inverse Hyperbolic Functions • Example 1 : sinh 3.6 M S 3.6 = 18.2854553600 • Example 2 : sinh1 30 M A j 30 = 앫13앫 4.09462222400 k Angle Unit Conversion • Press A v to display the following menu. R G 1 2 D 3 • Pressing 1 , 2, or 3 converts the displayed value to the corresponding angle unit. • Example : To convert 4.25 radians to degrees FFF1 →“ R ” 4 . 25 r 4.25 A v 2 (R) = 243.5070629 k Common and Natural Logarithms/ Antilogarithms • Example 1 : log 1.23 R 1.23 = 0.08990511100 • Example 2 : In 90 (loge 90) T 90 = 4.4998096700 • Example 3 : e10 A U 10 = 22026.4657900 • Example 4 : 101.5 A Q 1.5 = 31.622776600 2w 4= 16.00 • Example 5 : 24 k Square Roots, Cube Roots, Roots, Squares, Cubes, Reciprocals, Factorials, Random Numbers and π • Example 1: 2 3 5 L2+L3-L5= • Example 2: 3 5 3 5.28719690900 27 D 5 + D D 27 = –1.29002405300 앫14앫 1 • Example 3: 7 123 ( = 123 7 ) 7 A H 123 = 1.98864779500 • Example 4: 12330 2 123 + 30 K = 1023.00 12 N = 1728.00 R 3a, 4aT a= 12.00 8Af= 40320.00 • Example 5: 12 3 • Example 6: 1 1 1 3 4 • Example 7: 8! • Example 8: To generate a random number between 0.000 and 0.999 AM= 0.66400 Example (results differ each time) 3Ax= • Example 9: 3π 9.42477796100 k FIX, SCI, RND • Example 1: 200714400 (Specifies three decimal places.) 200 \ 7 - 14 = 400.00 FFFF13 400.00000 (Calculation continues using 10 display digits) Fix 200 \ 7 = 28.57100 - 14 = 400.00000 Performing the same calculation using the specified number of decimal places (Internal rounding) 200 \ 7 = 28.57100 AQ 28.57100 앫15앫 - 14 = 399.99400 • Press F F F F 3 1 to clear FIX specification. • Example 2: 1 3, displaying result with two significant digits (SCI 2) FFFF2 21 \3 = 3.3–01 Sci • Press F F F F 3 1 to clear SCI specification. k ENG Calculations • Example 1: To convert 56,088 meters to kilometers 56088 = J 56.088003 • Example 2: To convert 0.08125 grams to milligrams 0.08125 = J 81.25–03 k Inputting ENG Calculation Symbols • F F F F F 1 enters the ENG mode in which ENG symbols can be used in calculations. • To exit the ENG mode, press F F F F F 2. • The following are the nine ENG symbols that can be used in ENG mode calculations. Key Operation Ak AM Ag At Am AN An Ap Af Unit 103 106 109 1012 10–3 10–6 10–9 10–12 10–15 앫16앫 Symbol k (kilo) M (Mega) G (Giga) T (Tera) m (milli) µ (micro) n (nano) p (pico) f (femto) * For displayed values, the calculator selects the ENG symbol that makes the numeric part of the value fall within the range of 1 to 1000. * ENG symbols cannot be used when inputting fractions. * The ENG mode cannot be used in combination with the CMPLX, or BASE-N modes. • Performing any of the key operations in the above table while you are not in the ENG mode inputs the exponential value in the “Unit” column (without inputting the ENG symbol). • Example: 910 = 0.9 m (milli) 0. FFFFF1 9 \ 10 = ENG 9 1 m 900. In the ENG mode, even standard (non-ENG) calculation results are displayed using ENG symbols. AP J 0.9 9 1 m 900. k Coordinate Conversion (Pol(x, y), Rec (r, θ)) • Calculation results are automatically assigned to variables E and F. • Example 1: To convert polar coordinates (r2, 60°) to rectangular coordinates (x, y) (DEG mode) x A F 2 P 60 T = y 0o 1.00 R 1.73205080800 • 0 n, 0 o swaps displayed value with value in memory. • Example 2: To convert rectangular coordinates (1, 3) to polar coordinates (r, ) (RAD mode) r f1P L 3T= 앫17앫 2.00 T 0 o 1.04719755100 θ • 0 n, 0 o swaps displayed value with value in memory. k Permutation • Example: To determine how many different 4-digit values can be produced using the numbers 1 through 7 • Numbers cannot be duplicated within the same 4-digit value (1234 is allowed, but 1123 is not). 7Am4= 840. k Combination • Example: To determine how many different 4-member groups can be organized in a group of 10 individuals fx-115WA ................ 10 n 4 = 210. fx-991WA .......... 10 A n 4 = Statistical Calculations k Standard Deviation (SD Mode) • Press F F 1 to enter the SD Mode for statistical calculations using standard deviation. • Data input always starts with A m = to clear statistical memory. • Input data is used to calculate values for 0 1 Σx2 n, Σx, Σx2, o, σn and σn-1 which you can 0 2 Σx recall using the key operations noted 0 k n nearby. AM o A A σn A N σn-1 앫18앫 • Example: To calculate σn1, σn, o, n, Σx, and Σx 2 for the following data : 55, 54, 51, 55, 53, 53, 54, 52 Enter SD Mode F F 1 A m = (Memory Clear) 55 S 54 S 51 S 55 S 53 S S 54 S 52 S SD 52.00 (Sample Standard Deviation σ n1 ) A N = 1.40788595300 (Population Standard Deviation σn) A A = 1.31695671900 (Arithmetic Mean o) AM = 53.37500 (Number of Data n) 0k 8.00 Σx) 0H 427.00 0G 22805.00 (Sum of Values (Sum of Squares of Values Σx 2) Data Input Precautions • S S inputs the same data twice. • You can also input multiple entries of the same data using A G. To input the data 110 ten times, for example, press 110 A G 10 S . • The above results can be obtained in any order, and not necessarily that shown above. • To delete data you have just input, press A U. k Probability Distribution Calculations • Press A D to produce the screen shown below. P ( Q ( R ( →t 1 2 3 4 • Input a value from 1 to 4 to select the probability distribution calculation you want to perform. P(t) Q(t) 앫19앫 R(t) • Example : Using the x-data values input in the example on page 20, determine the normalized variate (→ t) for x = 53 and normal probability distribution P(t). 53 A D 4 (→t ) = -0.284747398 A D 1 ( P ( ) -0.28 F = 0.38974 k Regression Calculations (REG Mode) • Press F F 2 to enter the REG mode and then select one of the following regression types. 1 : Linear regression 2 : Logarithmic regression 3 : Exponential regression r 1 : Power regression r 2 : Inverse regression r 3 : Quadratic regression • Data input always starts with A m = to clear statistical memory. • The values produced by a regression calculation depend on the values input, and results can be recalled using the key operations shown in the table below. 0 G Σx 2 A N 0 H Σx A l 0k n Ad 0 h Σy 2 A c 0 n Σy A q 0 o Σxy A w 0 M Σx 3 A e 0 x Σx2y A J 0 y Σx 4 A O AM o Ab A A xσn xσn-1 p yσn yσn-1 Regression coefficient A Regression coefficient B Regression coefficient C Correlation coefficient r m n • Linear Regression The regression formula for linear regression is: y A Bx. 앫20앫 • Example: Atmospheric Pressure vs. Temperature Temperature Atmospheric Pressure 10°C 15°C 20°C 25°C 30°C 1003 hPa 1005 hPa 1010 hPa 1011 hPa 1014 hPa Perform linear regression to determine the regression formula terms and correlation coefficient for the data nearby. Next, use the regression formula to estimate atmospheric pressure at 18°C and temperature at 1000 hPa. Enter REG Mode (Linear Regression) qq21 A m = (Memory Clear) 10 P 1003 S 15 P 1005 S 20 P 1010 S 25 P 1011 S 30 P 1014 S 30.00 REG (Regression Coefficient A) A q= 997.400 (Regression Coefficient B) A w= 0.5600 (Correlation Coefficient r ) A J= 0.98260736800 (Atmospheric Pressure at 18°C) 18 A b 1007.4800 1000 A O 4.64285714300 (Temperature at 1000 hPa) • Quadratic Regression • The regression formula for quadratic regression is: y = A + Bx +Cx2. • Input data using the following key sequence. < x-data> P <y-data> S • Example: xi yi 29 50 74 103 118 1.6 23.5 38.0 46.4 48.0 Perform quadratic regression to determine the regression formula terms and correlation coefficient for the data nearby. Next, use the regression formula to estimate the values for ˆy (estimated value of y) for xi = 16 and ˆx (estimated value of x) for yi = 20. 앫21앫 Enter REG mode (Quadratic regression) FF2r3 A m= 29 P 1.6 S 50 P 23.5 S 74 P 38.0 S103 P 46.4 S 118 P 48.0 S 118. REG (Regression Coefficient A) A q = -35.59856934 (Regression Coefficient B) Aw= (Regression Coefficient C) A e = -6.71629667-03 1.495939413 (ˆy when x i = 16) 16 A b -13.38291067 (ˆx 1 when yi = 20) 20 A O 47.14556728 (ˆx 2 when yi = 20) AO 175.5872105 Data Input Precautions • S S inputs the same data twice. • You can also input multiple entries of the same data using A G. To input the data “20 and 30” five times, for example, press 20 P 30 A G 5 S. • The above results can be obtained in any order, and not necessarily that shown above. • To delete data you have just input, press A U. Complex Number Calculations (CMPLX Mode) • Press F 2 to enter the CMPLX Mode for calculations that include complex numbers. • You can use variables A, B, C and M only. Variables D, E, F, X, and Y are used for storage of the imaginary parts of values and so cannot be used by you. 앫22앫 • Example: (2 + 3i) + (4 + 5i ) Enter CMPLX Mode F 2 R2+3iT+ R 4+5iT= 6. Real number part Ar 8. i Imaginary number part k Absolute Value/Argument Calculation • The procedure described below can be used to determine the absolute value (Abs) and argument (arg) for a complex number of the format Z = a + bi , which is presumed to exist as coordinates on a Gaussian plane. • Example: To obtain the absolute value (r) and argument ( θ ) for the complex number 3 + 4i , when DEG is set for the angle unit mode Imaginary number axis Real number axis Determine the absolute value. AAR3+4i T= 5. CMPLX Determine the argument. A a R 3 + 4 i T = 53.13010235 Metric Conversions (fx-991WA) • A total of 20 different conversion pairs are built-in to provide quick and easy conversion to and from metric units. 앫23앫 • See the Conversion Pair Table shown below for a complete list of available conversion pairs. • Example: To convert 31 inches to centimeters 31 A c 01 CONV CONV 1 01 is the inches-to-centimeters conversion pair number. 31 i n cm 0. = 31 i n cm 78.74 • Conversion Pair Table Based on ISO Standard (1992) data and CODATA Bulletin 63 (1986) data. Number 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 Conversion Pair Number Conversion Pair in → cm cm → in ft → m m → ft yd → m m → yd mile → km km → mile n mile → m m → n mile acre → m2 m2 → acre r gal (US) →r r → gal (US) r gal (UK) →r r → gal (UK) pc → km km → pc km/h → m/s m/s → km/h 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 oz → g g → oz lb → kg kg → lb atm → Pa Pa → atm mmHg → Pa Pa → mmHg hp → kW kW → hp kgf/cm2 → Pa Pa → kgf/cm2 kgf•m → J J → kgf•m lbf/in2 → kPa kPa → lbf/in2 °F → °C °C → °F J → cal cal → J 앫24앫 Scientific Constants (fx-991WA) • A total of 40 commonly-used scientific constants, such as the speed of light in a vacuum and Planck's constant are built-in for quick and easy lookup whenever you need them. • Simply input the number that corresponds to the scientific constant you want to look up and it appears instantly on the display. • See the Scientific Constant Table shown below for a complete list of available constants. • Example: To determine how much total energy a person weighing 65kg has (E = mc 2) 65 L 28 CONST CONST28 28 is the “speed of light in vacuum” constant number. 65 Co 0. K 65 Co 2 0. 65 Co 2 = 5.841908662 18 • Scientific Constant Table Based on ISO Standard (1992) data and CODATA Bulletin 63 (1986) data. Number 01 02 03 04 05 06 07 08 09 Constant Name proton mass neutron mass electron mass muon mass Bohr radius Planck's constant nuclear magneton Bohr magneton Planck's constant, rationalized (h-bar) 앫25앫 Symbol mp mn me mµ a0 h µN µB Number 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Constant Name fine-structure constant classical electron radius electron Compton wavelength proton gyromagnetic ratio proton Compton wavelength neutron Compton wavelength Rydberg constant atomic mass unit proton magnetic moment electron magnetic moment neutron magnetic moment muon magnetic moment Faraday constant elementary charge Avogadro constant Boltzmann constant molar volume of ideal gas molar gas constant speed of light in vacuum first radiation constant second radiation constant Stefan-Boltzmann constant permittivity of vacuum permeability of vacuum magnetic flux quantum standard acceleration of gravity astronomical unit parsec Celsius temperature Newtonian constant of gravitation standard atmosphere Symbol α re λc γp λ cp λ cn R∞ u µp µe µn µµ F e NA k Vm R C0 C1 C2 σ ε0 µ0 φ0 g AU pc t G atm Base-n Calculations • In addition to decimal values, calculations can be performed using binary, octal and hexadecimal values. • You can specify the default number system to be applied to all input and displayed values, and the number system for individual values you input. 앫26앫 • You cannot use scientific functions in binary, octal, decimal, and hexadecimal calculations. You cannot input values that include decimal part and an exponent. • If you input a value that includes a decimal part, the unit automatically cuts off the decimal part. • Negative binary, octal, and hexadecimal values are produced by taking the two's complement. • You can use the following logical operators between values in Base-n calculations: and (logical product), or (logical sum), xor (exclusive logical sum), xnor (exclusive logical sum negation), Not (negation), and Neg (minus). • The following are the allowable ranges for each of the available number systems. 1000000000 0 Octal 4000000000 0 Decimal –2147483648 Hexadecimal 80000000 0 Binary x x x x x x x 1111111111 0111111111 7777777777 3777777777 2147483647 FFFFFFFF 7FFFFFFF • Example 1: To perform the following calculation and produce a binary result: 101112 + 11010 2 Binary mode FF3b 0. b 101112 + 110102 0. b = 110001. b • Example 2: To perform the following calculation and produce an octal result: 7654 8 ÷ 12 10 Octal mode FF3o 0. o l l l 4 (o) 76548 \ l l l 1 (d)1210 0. o = 516. o 앫27앫 • Example 3: To perform the following calculation and produce a hexadecimal result: 120 16 or 11012 Hexadecimal mode F F 3 h 0. 12016 l 2 (or) l l l 3 (b)11012 0. H 12d. H = H Degrees, Minutes, Seconds Calculations • You can perform sexagesimal calculations using degrees (hours), minutes, and seconds, and convert between sexagesimal and decimal values. • Example 1: To convert the decimal value 2.258 to a sexagesimal value 2.258 = 2.258 AO 2°15°28.8 • Example 2: To perform the following calculation: 12°34’56” 3.45 12 I 34 I 56 I - 3.45 0. = 43°24°31.2 Technical Information k When you have a problem...... If calculation results are not what you expect or if an error occurs, perform the following steps. 1. F 1 (COMP mode) 2. F F F 1 (DEG mode) 3. F F F F 3 1 (NORM 1 mode) 4. Check the formula you are working with to confirm it is correct. 앫28앫 5. Enter the correct modes to perform the calculation and try again. If the above steps do not correct the problem, press the key. The calculator performs a self-check operation and deletes all data stored in memory if any abnormality is detected. Make sure you always keep written copies of all important data. k Error Messages The calculator is locked up while an error message is on the display. Press t to clear the error, or press e or r to display the calculation and correct the problem. See “Error Locator” on page 9 for details. Ma ERROR • Cause • Calculation result is outside the allowable calculation range. • Attempt to perform a function calculation using a value that exceeds the allowable input range. • Attempt to perform an illogical operation (division by zero, etc.). • Action • Check your input values and make sure they are all within the allowable ranges. Pay special attention to values in any memory areas you are using. Stk ERROR • Cause • Capacity of the numeric stack or operator stack is exceeded. • Action • Simplify the calculation. The numeric stack has 10 levels and the operator stack has 24 levels. • Divide your calculation into two or more separate parts. Syn ERROR • Cause • Attempt to perform an illegal mathematical operation. 앫29앫 • Action • Press e or r to display the calculation with the cursor located at the location of the error. Make necessary corrections. Arg ERROR • Cause • Improper use of argument • Action • Press e or r to display the location of the cause of the error and make required corrections. k Order of Operations Calculations are performed in the following order of precedence. 1 Coordinate transformation: Pol (x, y), Rec (r , θ) 2 Type A functions: With these functions, the value is entered and then the function key is pressed. x2, x1, x!, ° ’ ” 3 Powers and roots: x y, x 4 a b/c 5 Abbreviated multiplication format in front of π, memory name, or variable name: 2π, 5A, πA etc. 6 Type B functions: With these functions, the function key is pressed and then the value is entered. 3 , , log, In, ex, 10x, sin, cos, tan, sin 1 , cos1, tan1, sinh, cosh, tanh, sinh 1, cosh1, tanh1, () 7 Abbreviated multiplication format in front of Type B functions: 2 3, Alog2 etc. 8 Permutation and combination: nPr, nCr 9 , 0 , * Operations of the same precedence are performed from right to left. exIn 120 → ex{In( 120)} Other operations are performed from left to right. * Operations enclosed in parentheses are performed first. 앫30앫 k Stacks This calculator uses memory areas, called “stacks,” to temporarily store values (numeric stack) and commands (command stack) according to their precedence during calculations. The numeric stack has 10 levels and the command stack has 24 levels. A stack error (Stk ERROR) occurs whenever you try to perform a calculation that is so complex that the capacity of a stack is exceeded. k Power Supply The TWO WAY POWER system actually has two power supplies: a solar cell and a G13 Type (LR44) button battery. Normally, calculators equipped with a solar cell alone can operate only when relatively bright light is present. The TWO WAY POWER system, however, lets you continue to use the calculator as long as there is enough light to read the display. • Replacing the Battery Either of the following symptoms indicates battery power is low, and that the battery should be replaced. • Display figures are dim and difficult to read in areas where there is little light available. • Nothing appears on the display when you press the key. • To replace the battery 1 Remove the six screws that Screw hold the back cover in place and then remove the back cover. 2 Remove the old battery. 3 Wipe off the sides of new battery with a dry, soft cloth. Load it into the unit with the positive k side facing up (so you can see it). 4 Replace the back cover and secure it in place with the six screws. 앫31앫 Screw 5 Press step. to turn power on. Be sure not to skip this • Auto Power Off Calculator power automatically turns off if you do not perform any operation for about six minutes. When this hapto turn power back on. pens, press 앫32앫 k Input Ranges Internal digits: 12 Accuracy: As a rule, accuracy is ±1 at the 10th digit. Functions sinx Input Range DEG 0 x 4.4999999991010 RAD 0 x 785398163.3 GRA 0 x 4.4999999991010 cosx DEG 0 x 4.5000000081010 RAD 0 x 785398164.9 GRA 0 x 5.0000000091010 tan x DEG Same as sinx, except when x= (2n-1)90. RAD Same as sinx, except when x= (2n-1)π/2. GRA Same as sinx, except when x= (2n-1)100. sin–1x cos–1x 0 x 1 tan–1x 0 x 9.9999999991099 sinhx coshx 0 x 230.2585092 sinh x 0 x 4.9999999991099 –1 cosh–1x tanhx tanh–1x 0 x 9.99999999910-1 log x/ln x 0 x 10 x –9.9999999991099 x 99.99999999 ex x x2 1/x 3 x x! –9.9999999991099 x 230.2585092 0 x 1 10100 x 1 1050 x 1 10100 ; x G 0 x 1 10100 0 x 69 (x is an integer) 앫33앫 Functions Input Range nP r 0 n 99, r n (n, r is an integer)99 1 {n!/( n–r)!} 9.99999999910 nCr 0 n 99, r n (n, r is an integer) 49 Pol(x, y) x, y 9.99999999910 (x2 +y2 ) 9.99999999910 99 99 Rec(r, ) 0 r 9.99999999910 θ: Same as sinx, cosx °’ ” xy x y a b/c SD (REG) a, b, c 110100 0 b, c x110100 Decimal ↔ Sexagesimal Conversions 00 0000 x 9999990 590 x0: –110100ylogx100 x0: y0 1 x0: yn, 2n+1 ( n is an integer) However: –110 100 ylogx100 y0: x G 0 –1101001/x logy100 y0: x0 1 y0: x2n1, n (n G 0; n is an integer) However: –110 100 1/x logy100 Total of integer, numerator, and denominator must be 10 digits or less (including division marks). x 11050 y 11050 n 110100 xn, yn, o, p A, B, r : n G 0 xn–1, yn–1 : n G 0, 1 * Erros are cumulative with such internal continuous calx 3 culations as x y, x , x!, and x , so accuracy may be adversely affected. 앫34앫 Specifications Power Supply: Solar cell and a single G13 Type button battery (LR44) Battery Life: Approximately 3 years (1 hour use per day). Dimensions: 10(H)76(W)150(D) mm 3 /8⬙(H)3⬙(W)57/8 ⬙(D) Weight: 85 g (3 oz) including battery Power Consumption: 0.0001W Operating Temperature: 0°C ~ 40°C (32°F ~ 104°F) 앫35앫 CASIO COMPUTER CO., LTD. 6-2, Hon-machi 1-chome Shibuya-ku, Tokyo 151-8543, Japan U.S. Pat. 4,410,956 SA9911-A Printed in China HA310537-1

Download PDF

- Similar pages
- Resetting the CASIO fx-9750GII for testing purposes
- Casio FX-570D User`s guide
- Calculating on the Casio cfx-9850G Plus
- Resetting the PRIZM
- Casio fx-300W User`s guide
- Casio FX-95 User`s guide
- Casio FX-100D User`s guide
- Casio FX-912MS Calculator User Manual
- E – 1 General Guide ................................................. 3 Before Starting
- Quick Start Guide Model: 1228-2
- Casio FX-820MS User`s guide
- Casio FX-85SA User`s guide
- fx-95MS fx-100MS fx-570MS fx-991MS
- 4325 SPEC SHEET front.ai
- SR270ll / SR-275 Scientific Calculator
- Statistics Using the CFX-9850GB Plus Calculator
- Casio fx-350MS Product specifications
- QS-2130 Operation Manual
- Casio 3950P User`s guide
- Casio FX-115MS - ADDITIONAL FUNCTIONS User`s guide
- ATDIDT User's guide
- Aurora AX-582BL