E fx-820MS User's Guide http://world.casio.
CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Circular Road, London NW2 7JD, U.K.
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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 battery from the calculator, put it in a safe place where it will not get into the hands of small children and accidentally swallowed. • Keep batteries out of the reach of small children.
• 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.
• • • • • Take care never to leave the calculator where it might be splashed by water or exposed to large amounts of humidity or dust. Such conditions 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.
Contents Safety Precautions .................................. 2 Handling Precautions ............................. 3 Two-line Display ...................................... 7 Before getting started... .......................... 7 kModes .................................................................... 7 kInput Capacity ........................................................ 8 kMaking Corrections During Input ........................... 8 kReplay Function ................................................
kAngle Unit Conversion ......................................... 20 kCoordinate Conversion (Pol (x, y), Rec (r, θ )) ..... 21 kEngineering Notation Calculations ....................... 21 Statistical Calculations ......................... 22 Standard Deviation .................................................. 22 Regression Calculations .......................................... 24 Technical Information ........................... 28 kWhen you have a problem...... .............................
Two-line Display The two-line display makes it possible to view both the calculation formula and its result at the same time. • The upper line shows the calculation formula. • The lower line shows the result. A separator symbol is displayed every three digits when the integer part of the mantissa has more than three digits. Before getting started... k Modes Before starting a calculation, you must first enter the correct mode as indicated in the table below.
Note! • To return the calculation mode and setup to the initial defaults shown below, press A B 2(Mode) =. Calculation Mode: Angle Unit: Exponential Display Format: Fraction Display Format: Decimal Point Character: COMP Deg Norm 1 ab/c Dot • Mode indicators appear in the upper part of the display. • Be sure to check the current calculation mode (SD, REG, COMP) and angle unit setting (Deg, Rad, Gra) before beginning a calculation.
k Replay Function • Every time you perform a calculation, the replay function stores the calculation formula and its result in replay memory. Pressing the [ key displays the formula and result of the calculation you last performed. Pressing [ again back steps sequentially (new-to-old) through past calculations. • Pressing the e or r key while a replay memory calculation is on the display changes to the editing screen.
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. • To change the exponential display format, press the F key a number of times until you reach the exponential display format setup screen shown below. F i x Sc i No r m 1 2 3 • Press 3.
• Press the number key ( 1 or 2 ) that corresponds to the setting you want to use. 1(Dot): Period decimal point, comma separator 2(Comma): Comma decimal point, period separator k Initializing the Calculator • Perform the following key operation when you want to initialize the calculation mode and setup, and clear replay memory and variables. A B 3 (All) = Basic Calculations COMP k Arithmetic Calculations Use the F key to enter the COMP Mode when you want to perform basic calculations. COMP ...........
• Example 1: 13 2 1 15 3 5 2C3+1C5= 13 15.00 1 2 11 • Example 2: 3 1 4 4 3 12 3C1C4+ 1C2C3= 4 11 12.00 2 1 • Example 3: 4 2 • Example 4: 2C4= 1 1.6 2.1 2 1 C 2 + 1.6 = • Results of calculations that mix fraction and decimal values are always decimal. uDecimal ↔ Fraction Conversion • Use the operation shown below to convert calculation results between decimal values and fraction values. • Note that conversion can take as long as two seconds to perform. 3 • Example 1: 2.
uMixed Fraction ↔ Improper Fraction Conversion • Example: 1 2 5 ↔ 3 3 1C 2C 3= 1 2 3.00 AB 5 3.00 AB 1 2 3.00 • You can use the display setup (Disp) screen to specify the display format when a fraction calculation result is greater than one. • To change the fraction display format, press the q key a number of times until you reach the setup screen shown below. Disp 1 • Display the selection screen. 1 • Press the number key ( 1 or 2) that corresponds to the setting you want to use.
• Example 4 : To discount 3500 by 25% (2625) 3500 - 25 A v , • Example 5 : To discount the sum of 168, 98, and 734 by (800) 20% 168 + 98 + 734 = g A j q p q - 20 A v , * * As shown here, if you want to use the current Answer Memory value in a mark up or discount calculation, you need to assign the Answer Memory value into a variable and then use the variable in the mark up/discount calculation.
• Example 2: To perform the following calculation: 12°34’56” 3.45 12 I 34 I 56 I - 3.45 = 43°24°31.2 k FIX, SCI, RND • To change the settings for the number of decimal places, the number of significant digits, or the exponential display format, press the F key a number of times until you reach the setup screen shown below. F i x Sc i No r m 1 2 3 • Press the number key ( 1, 2, or 3) that corresponds to the setup item you want to change.
• Example 2: 1 3, displaying result with two significant digits (Sci 2) F ..... 2 (Sci) 2 1 \ 3 = SCI 3.3–01 • Press F ..... 3 (Norm) 1 to clear the Sci specification. Memory Calculations COMP Use the F key to enter the COMP Mode when you want to perform a calculation using memory. COMP .............................................................
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 A j 3.
Scientific Function Calculations COMP Use the F key to enter the COMP Mode when you want to perform basic arithmetic calculations. COMP ............................................................. F 1 • Certain types of calculations may take a long time to complete. • Wait for the result to appear on the display before starting the next calculation. • π = 3.
• Example 3 : cos 1 2 π (rad) 0.25 π (rad) 2 4 ( ) q ..... 2 (Rad) A V RL2 \ 2T =g \ A x = • Example 4: tan 1 0.741 36.53844577 ° q ..... 1 (Deg) A g 0.741 = k Hyperbolic/Inverse Hyperbolic Functions • Example 1: sinh 3.6 18.28545536 M S 3.6 = • Example 2: sinh 1 30 4.094622224 M A j 30 = k Common and Natural Logarithms/ Antilogarithms • Example 1: log 1.23 0.089905111 R 1.23 = • Example 2: In 90 (= loge 90) = 4.49980967 T 90 = TpP= ln e 1 • Example 3: e10 22026.
• Example 2: 3 • Example 3: 7 5 3 27 –1.290024053 A D 5 + A D R D 27 T = 1 123 ( = 123 7 ) 1.988647795 7 A H 123 = • Example 4: 123 30 2 1023 123 + 30 K = 12 N = • Example 5: 123 1728 1 • Example 6: 12 1 1 3 4 R3a,4aTa= • Example 7: 8! 40320 8Af= • Example 8: To generate a random number between 0.000 and 0.999 AM= 0.66400 (The above value is a sample only. Results differ each time.) • Example 9: 3π 9.
• Example: To convert 4.25 radians to degrees q ..... 1(Deg) 4 . 25 r 4.25 A v 2(R) = 243.5070629 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 (r 2, 60°) to rectangular coordinates (x, y) (Deg) x 1 A F 2 P 60 T = 0o y 1.732050808 • Press 0 n to display the value of x, or 0 o to display the value of y.
SD REG Statistical Calculations SD Standard Deviation Use the F key to enter the SD Mode when you want to perform statistical calculations using standard deviation. SD ................................................................... F 2 • Always start data input with A B 1 (Scl) = to clear statistical memory. • Input data using the key sequence shown below. < x-data> S • Input data is used to calculate values for n, Σx, Σx2, o, σn and σn-1, which you can recall using the key operations noted nearby.
A X 1= A U 3= A U 2= A U 1= Arithmetic Mean (o ) = 53.375 Number of Data ( n) = 8 Sum of Values (Σx ) = 427 Sum of Squares of Values ( Σx2 ) = 22805 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. • You can perform the above key operations in any order, and not necessarily that shown above.
Press 2 to exit data input without registering the value you just input. Press 1 if you want to register the value you just input, without saving it in memory. If you do this, however, you will not be able to display or edit any of the data you have input. • To delete data you have just input, press A U . • After inputting statistical data in the SD Mode or REG Mode, you will be unable to display or edit individual data items any longer after perform either the following operations.
• Always start data input with A B 1 (Scl) = to clear statistical memory. • Input data using the key sequence shown below. < x-data> P S • 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.
• The values in the above tables can be used inside of expressions the same way you use variables. uLinear Regression • The regression formula for linear regression is: y = A + Bx. • 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.
Coefficient of Determination = 0.965517241 AXrr3K= E A Ur 3, AU3-AX1AXr1F\ EAU3,1F= Sample Covariance = 35 uLogarithmic, Exponential, Power, and Inverse Regression • Use the same key operations as linear regression to recall results for these types of regression. • The following shows the regression formulas for each type of regression.
Regression Coefficient C = – 6.71629667 10 –3 AXrr3= n when xi is 16 = –13.38291067 16 A X r r r 3 = m1 when y i is 20 = 47.14556728 20 A X r r r 1 = m2 when y i is 20 = 175.5872105 20 A X r r r 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 “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.
Math ERROR • Causes • Calculation result is outside the allowable calculation range. • An attempt to perform a function calculation using a value that exceeds the allowable input range. • An 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. Stack ERROR • Cause • The capacity of the numeric stack or operator stack is exceeded.
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. x3, x2 , x 1, x!, ° ’ ” m, m1, m2 , n Angle unit conversions (DRG') 3 Powers and roots: ^ (xy), x 4 a b/c 5 Abbreviated multiplication format in front of π, e (natural logarithm base), memory name, or variable name: 2π, 3e, 5A, πA, etc.
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 (Stack ERROR) occurs whenever you try to perform a calculation that is so complex that the capacity of a stack is exceeded.
k Input Ranges Internal digits: 12 Accuracy*: As a rule, accuracy is ±1 at the 10th digit. Functions sinx Input Range DEG 0 x 4.499999999 1010 RAD 0 x 785398163.3 GRA 0 x 4.999999999 1010 cosx DEG 0 x 4.500000008 1010 RAD 0 x 785398164.9 GRA 0 x 5.000000009 1010 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 9.999999999 1099 sinhx coshx 0 x 230.
Functions nCr Input Range 0 n 1 1010, 0 r n (n, r are integers) 1 [n!/{ r!( n–r )!}] 1 10 100 x , y 9.999999999 1049 (x2 +y2 ) 9.999999999 10 99 0 r 9.
In the vicinity of a function’s singular point and point of inflection, errors are cumulative and may become large. 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.
Auto Power Off Calculator power automatically turns off if you do not perform any operation for about six minutes. When this happens, press 5 to turn power back on. Specifications Power Supply: Solar cell and a single G13 Type button battery (LR44) Battery Life: Approximately 3 years (1 hour use per day) Dimensions: 12.0 (H) 89.0 (W) 173.0 (D) mm 1 /2⬙ (H) 3 1 /2⬙ (W) 6 13/16⬙ (D) Weight: 120 g (4.23 oz) including battery Power Consumption: 0.
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