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Casio fx-115ES, fx-991ES kCalculation Ranges, Number of Digits, and Precision, Stack Issues to Keep in Mind for Each Mode

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A Stack ERROR occurs when the calculation you are performing causes the capacity of either stack to be exceeded.

Stack Issues to Keep in Mind for Each Mode

•In the CMPLX Mode, each input value uses two levels of the numeric stack, regardless of whether the input value is a real number or a complex number. This means that the numeric stack effectively has only five levels in the CMPLX Mode.

•The MATRIX Mode uses its own matrix stack, which is used in combination with the general-purpose numeric stack.The matrix stack has three levels. Performing a calculation that involves a matrix causes one level of the matrix stack to be used for storage of the result. Squaring, cubing, or inverting a matrix also uses one level of the matrix stack.

•The VECTOR Mode uses its own vector stack, which is used in combination with the general-purpose numeric stack. The vector stack has five levels.Vector stack usage follows the same rules as the matrix stack, described above.

kCalculation Ranges, Number of Digits, and Precision

The calculation range, number of digits used for internal calculation, and calculation precision depends on the type of calculation you are performing.

Calculation Range and Precision

	Calculation Range			±1 ⋅ 10–99to ±9.999999999 ⋅ 1099 or 0
	Number of Digits for Internal			15 digits
	Calculation			15 digits
	Calculation

	Precision			In general, ±1 at the 10th digit for a single
				calculation. Precision for exponential display
				is ±1 at the least significant digit. Errors are
				cumulative in the case of consecutive
				calculations.
	Function Calculation Input Ranges and Precision

	Functions			Input Range
	sinx	DEG	0 x 9109
		RAD	0 x 157079632.7
		GRA	0 x 11010
	cosx	DEG	0 x 9109
		RAD	0 x 157079632.7
		GRA	0 x 11010
	tanx	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	0 x 1
	cos–1x	0 x 1
	cos–1x
	tan–1x	0 x 9.9999999991099
	sinhx	0 x 230.2585092
	coshx	0 x 230.2585092
	coshx
	sinh–1x	0 x 4.9999999991099
	cosh–1x	1 x 4.9999999991099

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Contents

Page Page About this Manual Initializing the Calculator Safety Precautions Handling Precautions Before Using the Calculator kAbout the Display kDisplay Indicators Sample Display: This Means this: Calculation Modes and Calculator Setup Specifying the Calculation Mode Specifying the Input/Output Format Specifying the Default Angle Unit Specifying the Number of Display Digits Specifying the Fraction Display Format Specifying the Complex Number Display Format Specifying the Statistical Display Format Specifying the Decimal Point Display Format Inputting Expressions and Values Inputting a Function with Parenthesis Omitting the Multiplication Sign Final Closed Parenthesis Displaying a Long Expression Number of Input Characters (Bytes) About the Insert and Overwrite Input Modes Changing the Character or Function You Just Input Deleting a Character or Function Correcting a Calculation Inserting Input into a Calculation kDisplaying the Location of an Error kInputting with Math Format Functions and Symbols Supported for Math Format Input Math Format Input Examples Incorporating a Value into a Function Displaying Calculation Results in a Form that Includes , etc Example 2: sin (60) Example 3: sin–1 (0.5) Angle Unit k 'Form Calculation Range Reasons why the results of the examples are displayed in decimal form Basic Calculations Number of Decimal Places and Number of Significant Digits Omitting a Final Closed Parenthesis Switching between Improper Fraction and Mixed Fraction Format Switching between Fraction and Decimal Format Inputting Sexagesimal Values Sexagesimal Calculations Converting Values between Sexagesimal and Decimal Using Multi-statementsin Calculations Using Calculation History Memory and Replay Recalling Calculation History Memory Contents Replay Function Using Calculator Memory Answer Memory Overview Using Answer Memory to Perform a Series of Calculations Inputting Answer Memory Contents into an Expression Independent Memory Overview Calculation Examples Using Independent Memory Clearing Independent Memory Variable Overview Clearing the Contents of a Specific Variable Using CALC uExpressions that contain variables uMulti-statements uExpressions with a single variable on the left Using SOLVE Precautions when Using SOLVE Solution Screen Contents Continue Screen Function Calculations kConverting an Input Value to the Calculator’s Default Angle Unit kExponential Functions and Logarithmic kPower Functions and Power Root kIntegration Calculations Tips on Improving Integration Value Accuracy kDifferential Calculations kΣ Calculations kRectangular-PolarCoordinate Conversion Converting to Polar Coordinates (Pol) Converting to Rectangular Coordinates (Rec) Factorial (!) Absolute Value Calculation (Abs) Random Number (Ran#) Permutation (nPr) and Combination (nCr) Rounding Function (Rnd) Transforming Displayed Values Formats Supported for S-DTransformation Examples of S-DTransformation Complex Number Calculations Examples of Calculation Results Using Rectangular Coordinate Format (a + bi) Examples of Calculation Results Using Polar Coordinate Format (r ∠ θ) Specifying the Calculation Result Display Format Statistical Calculation (STAT) Selecting a Statistical Calculation Type Displaying the STAT Editor Screen STAT Editor Screen FREQ (Frequency) Column Rules for Inputting Sample Data on the STAT Editor Screen STAT Editor Screen Input Precautions Precautions Concerning Sample Data Storage Editing Sample Data STAT Menu Items Single-variable (1-VAR)Statistical Calculation Commands Distr Sub-menu(11(STAT)7(Distr)) Standard Normal Distribution Commands when Linear Regression Calculation (A+BX) Is Selected Commands when Quadratic Regression Calculation (_+CX2) Is Selected Comments for Other Types of Regression Command Usage Tips Base-n Calculations Inputting Values Inputting Hexadecimal Values Value Ranges Specifying the Base during Input Equation Calculations Changing the Current Equation Type Setting Rules for Inputting and Editing Coefficients Initializing All Coefficients to Zero Coefficient Editor Screen Input Precautions Matrix Calculations Creating a Matrix and Storing It in Matrix Memory Copying the Contents of One Matrix to Another Matrix Matrix Answer Memory Screen kMatrix Menu Items Generating a Number Table from a Function kSupported Function Types kStart, End, and Step Value Rules Vector Calculations (VECTOR) Creating a Vector and Saving It in Vector Memory Copying the Contents of One Vector to Another Vector Vector Answer Memory Screen Scientific Constants Metric Conversion Technical Information kCalculation Priority Sequence kStack Limitations kCalculation Ranges, Number of Digits, and Precision Page kError Messages Page kBefore assuming malfunction of the calculator Reference Replacing the Battery Auto Power Off Specifications CASIO COMPUTER CO., LTD