Ebidyaloy · Scientific Calculator Emulator
SC-991BF
WindowsmacOSWebAndroidiOS
SHIFT
VARIABLE
FUNCTION
CATALOG
TOOLS
QRx
▢¾▢∕▢
∛▢√▢
▢³▢²
▢√▢▢^
10ˣlog
eˣln
Ans
sin⁻¹sin
cos⁻¹cos
tan⁻¹tan
%(
,)
π7
e8
i9
INSDEL
OFFAC
4A
5B
6C
nPr×
nCr÷
1D
2E
3F
°’”+
(−)−
0x
.y
×10ˣz
⇄
≈EXE
Complete User's Guide & Function Reference — everything you need to operate the SC-991BF scientific calculator emulator, with every example result computed by the calculator engine.
About This Guide
WelcomeSC-991BF Emulator
The eBidyaloy SC-991BF is an on-screen scientific calculator emulator for classrooms and study — available on Windows, macOS, Web, Android and iOS. It reproduces a modern ClassWiz-style scientific calculator: a natural “textbook” display, 13 calculator apps, physical constants, unit conversions, and a live step-by-step explainer for teaching.
Throughout this guide, every worked Example shows the expression, the calculator display, and the exact key operation. All results are produced by the actual SC-991BF calculation engine, so what you read here is what the emulator computes.
How to read the key operations
Key presses are shown as chips, e.g. 7 × 8 EXE. A key’s SHIFT function (orange label above the key) is written SHIFT then the key; a VARIABLE letter (gold) is entered from the VARIABLE menu.
Keys & Key Markings
The FaceplateZones
The SC-991BF keypad is arranged in the same zones as a modern scientific calculator: a title strip, the LCD, a control cluster, five soft keys, two scientific rows, and the number pad.
SHIFT
VARIABLE
FUNCTION
CATALOG
TOOLS
QRx
▢¾▢∕▢
∛▢√▢
▢³▢²
▢√▢▢^
10ˣlog
eˣln
Ans
sin⁻¹sin
cos⁻¹cos
tan⁻¹tan
%(
,)
π7
e8
i9
INSDEL
OFFAC
4A
5B
6C
nPr×
nCr÷
1D
2E
3F
°’”+
(−)−
0x
.y
×10ˣz
⇄
≈EXE
Key Markings — three functions per key
Most keys have up to three functions:
7 Primary — printed on the key; press it directly.
π SHIFT — the orange label above the key; press SHIFT first, then the key.
A VARIABLE — the gold letter; entered from the VARIABLE menu.
For example, SHIFT 7 inputs π, and SHIFT sin inputs sin⁻¹.
Control Cluster
| Key | Function |
|---|
| ON | Turns the calculator on and clears the current entry (AC also clears). |
| ⌂ HOME | Opens the HOME screen — the menu of all calculator apps. |
| ⚙ SETTINGS | Opens the SETTINGS menu (Calc Settings and Reset). |
| ↺ Back | Deletes the character before the cursor, or steps back one menu level. |
| ▲ ▼ ◀ ▶ | Cursor keys — move the entry cursor, or move the highlight in menus and tables. |
| OK | Executes the calculation or selects the highlighted menu item (same as EXE). |
| ⤒ ⤓ | Page keys — jump to the top / bottom of a long result, menu, table or list. |
Soft Keys
| Soft key | Opens |
|---|
| SHIFT | Selects the alternate (orange) function printed above the next key you press. |
| VARIABLE | The variable menu — recall or store the memories A, B, C, D, E, F, x, y, z and M (M also has M+ / M−). |
| FUNCTION | A function menu for the current app (e.g. Abs, arg, Conjg, ReP, ImP for complex work). |
| CATALOG | The CATALOG of commands and functions, plus CONST ▸ (physical constants) and CONV ▸ (unit conversions). |
| TOOLS | Result tools: S⇔D, Prime Factor, Recurring Decimal, Sexagesimal (° ’ ”) and Improper Fraction. |
Scientific Keys
| Key | SHIFT | Function |
|---|
| x | QR | Inserts the variable x. |
| ▢∕▢ | ▢¾ | Fraction template a⁄b. SHIFT inserts a mixed-number template. |
| √▢ | ∛▢ | Square root. SHIFT inserts a cube root. |
| ▢² | ▢³ | Square (x²). SHIFT cube (x³). |
| ▢^ | ▢√▢ | Power xʸ. SHIFT the x-th root of a value. |
| log | 10ˣ | Common logarithm (base 10). SHIFT raises 10 to a power. |
| ln | eˣ | Natural logarithm (base e). SHIFT raises e to a power. |
| Ans | — | Inserts the previous answer. |
| sin | sin⁻¹ | Sine. SHIFT arcsine (inverse). |
| cos | cos⁻¹ | Cosine. SHIFT arccosine (inverse). |
| tan | tan⁻¹ | Tangent. SHIFT arctangent (inverse). |
| ( | % | Open parenthesis. SHIFT the percent operator. |
| ) | , | Close parenthesis. SHIFT a comma (argument separator). |
Number Pad
| Key | SHIFT | VARIABLE | Function |
|---|
| 7 8 9 | π e i | — | Digits. SHIFT: 7→π, 8→e, 9→i (imaginary unit). |
| 4 5 6 | — | A B C | Digits, or recall variables A / B / C via VARIABLE. |
| 1 2 3 | — | D E F | Digits, or recall variables D / E / F via VARIABLE. |
| 0 . | — | x y | Digit / decimal point, or variables x / y. |
| DEL | INS | — | Deletes at the cursor. SHIFT toggles insert mode. |
| AC | OFF | — | All clear. SHIFT turns the calculator off. |
| × | nPr | — | Multiply. SHIFT permutation (nPr). |
| ÷ | nCr | — | Divide. SHIFT combination (nCr). |
| + | ° ’ ” | — | Add. SHIFT sexagesimal (degrees-minutes-seconds) entry. |
| − | (−) | — | Subtract. SHIFT the negative sign for a signed value. |
| ×10ˣ | — | z | Enters a power-of-ten exponent (scientific entry). VARIABLE: z. |
| ⇄ (FORMAT) | — | — | S⇔D: toggles the result between decimal and exact (fraction / √ / π) form. Opens the FORMAT menu when set to do so. |
| EXE | ≈ | — | Executes the calculation. SHIFT forces a decimal (≈) result. |
Menu-Operation Shorthand
To keep instructions short, this guide writes menu paths in a compact form. For example:
⚙ − [Calc Settings] > [Angle Unit] > [Degree]
…is the same as the full operation:
1. Press ⚙.
2. Use ▲ ▼ to select [Calc Settings], then press OK.
3. Select [Angle Unit], then press OK.
4. Select [Degree], then press OK.
NoteWhere a menu item shows an option number to its left, you can also press that number key to jump straight to the item — see Using Menus.
Entering & Editing Calculations
Entering a CalculationNatural textbook input
The SC-991BF uses a natural textbook display (MathI/MathO): fractions, roots, powers and other expressions appear on screen just as they are written on paper. You type an expression from left to right and press EXE to evaluate it.
Keys such as ▢∕▢ (fraction), √▢ (root) and ▢^ (power) insert an empty template with boxes to fill. Type into the highlighted box, and press ▶ to move out of it and continue the calculation.
Example 1To enter 1½ + √4
SHIFT ▢∕▢ 1, 1, 2 ▶ + √▢ 4 ▶ EXE
The mixed-number template SHIFT ▢∕▢ creates three boxes (whole, numerator, denominator); ▶ steps out of the root before EXE. The result 1.5 + 2 = 3.5 is shown.
Editing a CalculationCursor, insert & delete
Moving the cursor
Use the arrow keys to move the flashing cursor through an expression without erasing anything:
| Key | Movement |
| ◀ ▶ | Move left / right one item along the current line. |
| ▲ ▼ | Move between levels of a template — for example up into the numerator of a fraction or down into the denominator. |
Deleting and inserting
To correct a mistake, move the cursor to the spot and use:
| Key | Action |
| DEL | Delete the item immediately to the left of the cursor. |
| SHIFT DEL (INS) | Toggle between insert mode (new input pushes existing items right) and overwrite mode. |
| AC | Clear the whole expression and start again. |
Example 2To fix 7 × 9 typed as 7 × 8
◀ DEL 9 EXE
With the cursor after the 8, press DEL to remove it, type 9, then EXE. Only the wrong digit is changed — the rest of the expression is untouched.
NoteThe calculator inserts by default, so you rarely need overwrite mode. If new characters seem to replace what is already there, press SHIFT DEL (INS) once to switch back to insert.
Correcting after a result
After you press EXE and see a result, you have two choices:
- Begin a new calculation — just start typing, and the previous entry is cleared.
- Edit the previous entry — press ◀ or ▶ to bring the expression back with the cursor in it, change what you need, and press EXE again.
Calculation HistoryRecall & replay
The calculator keeps your last 30 calculations. From a result, press ▲ to step back through previous entries and ▼ to step forward. A recalled entry can be re-used in two ways:
- Press EXE to re-run the recalled calculation as it is.
- Move the cursor into it, edit the expression, then press EXE to evaluate the changed version.
Example 3To recall and re-run a previous calculation
at a result → ▲ browse → EXE re-run
Pressing ▲ brings back an earlier entry such as 7 × 8 − 4 × 5; EXE evaluates it again. Editing it first lets you try a variation without retyping the whole line.
Important!Calculation history is cleared when you switch to a different app or reset the calculator. Use a variable (Store into A–F, x, y, z, M) to keep a value you will need after leaving the app.
Reusing the last answer with Ans
The result of the most recent calculation is held in Ans. Start a new calculation with an operator (for example + or ×) and the calculator inserts Ans automatically, or press Ans to use it anywhere in an expression.
Example 4To chain calculations with Ans
1000 − 200 EXE → × 2 EXE
After 1000 − 200 = 800, pressing × 2 continues from that answer: Ans × 2 = 1600. This lets you build up a long calculation one step at a time.
Using the CATALOG
Using the CATALOG MenuCommands & Functions
Press CATALOG to open a scrollable list of the commands, functions and symbols available in the current app. Move the highlight with ▲ ▼ and press OK to insert the selected item; press ↺ to close.
CATALOG
d/dx( derivative
∫( integral
Σ( summation
GCD( LCM(
CONST ▸▸
CONV ▸▸
Two entries open sub-menus: CONST ▸ (physical constants) and CONV ▸ (unit conversions). Everything else is inserted straight into your calculation.
NoteOn the SC-991BF, CATALOG is a single combined list of commands (plus the CONST ▸ and CONV ▸ sub-menus). The groups in the table below are a reading aid — on-screen you simply scroll one list.
CATALOG commands
| Group | Commands available from CATALOG |
|---|
| Function Analysis | d/dx( derivative · ∫( integral · Σ( summation · Π( product · log▢(▢) log to any base · x⁻¹ reciprocal · x! factorial |
| Numeric | GCD( · LCM( · RanInt#( random integer · Pol( rectangular→polar · Rec( polar→rectangular · Abs · Int/Frac/Intg/Rnd |
| Hyperbolic | sinh · cosh · tanh · sinh⁻¹ · cosh⁻¹ · tanh⁻¹ |
| Special operations | SOLVE (f(x)=0) · CALC (evaluate with variables) · FACT (prime factorise) · ENG / ENG→ (engineering form) · RECUR (recurring decimal) · VERIFY (test a relation) |
| Symbols | : multi-statement · → store to variable · =, ≠, <, >, ≤, ≥ relations · ° ʳ ᵍ angle units |
| Matrix / Vector | MatA–MatD, MatAns · VctA–VctD, VctAns · det( · Trn( transpose · Identity( |
| Reference ▸ | CONST ▸ 47 physical constants (6 categories) · CONV ▸ 40 unit conversions (9 categories) |
CONST — Physical ConstantsCATALOG → CONST ▸
CONST ▸ opens a menu of 47 scientific constants (CODATA-2022) organised into six categories. Choose a category, then a constant, to insert its symbol and value into your calculation.
CONST
❶Universal▸
❷Electromagnetic▸
❸Atomic & Nuclear▸
❹Physico-Chem▸
For example, inserting c (speed of light) inserts the value 299 792 458. The complete list appears in the Constants & Conversions reference chapter.
CONV — Unit ConversionsCATALOG → CONV ▸
CONV ▸ applies a unit conversion to the value currently on the display. First compute a value, then choose a category and a conversion; the result is replaced by the converted value.
UNIT CONVERT
❶Length▸
❷Area▸
❸Volume▸
❹Mass▸
There are 40 conversions across nine categories (Length, Area, Volume, Mass, Velocity, Pressure, Energy, Power, Temperature). The full list is in the reference chapter.
Example — greatest common divisor from CATALOG
To compute the GCD of 12 and 18:
CATALOG›GCD(›1›2›,›1›8›)›EXE
Result: GCD(12, 18) = 6. The same menu provides LCM, random integers, and the Pol/Rec coordinate conversions.
Calculator Apps
Selecting a Calculator AppHOME screen
Press ⌂ to display the HOME screen — the menu of all installed calculator apps. Use ▲ ▼ ◀ ▶ to move the highlight to an app, then press OK. Alternatively, press the number key shown on an app’s icon (its option number) to open it directly.
NoteEach app remembers its own screen, data and CATALOG. Switching apps does not clear another app’s data.
Installed Calculator App List13 apps
| App | Description |
|---|
| General and scientific calculations — arithmetic, functions, powers, roots, logs, complex numbers and every CATALOG command. |
| 1- and 2-variable statistics and seven regression models, with a data-entry table and a full set of summary results. |
| Generates a table of values from one or two functions, f(x) and g(x), over a start/end/step range. |
| Solves simultaneous linear equations (2 to 4 unknowns) and polynomial equations (quadratic, cubic, quartic). |
| Solves quadratic, cubic and quartic inequalities and reports the solution intervals. |
| Normal, Binomial and Poisson probability — both probability density (PD) and cumulative distribution (CD). |
| Dedicated complex-number arithmetic with rectangular (a + bi) and polar (r∠θ) results. |
| Matrix arithmetic up to 4×4 — addition, subtraction, multiplication, determinant, inverse and transpose. |
| 2D and 3D vector operations — dot product, cross product, magnitude, angle and unit vectors. |
| A 5-column (A–E) × 45-row spreadsheet with cell formulas, fill/copy tools and range functions (Sum, Min, Max, Mean). |
| Solves proportions of the form a : b = c : x for the unknown term. |
| Probability and learning tools — dice roll, coin toss, number line and circle simulations. |
| Binary, octal, decimal and hexadecimal calculations with logic operators (and, or, xor, not). |
App Screens at a GlanceEntry screens
When you open an app you see either a calculation screen or a short menu to choose the calculation type. Each app is documented in full — every function with worked examples — in the chapters that follow.
App 1
Calculate
General and scientific calculations — arithmetic, functions, powers, roots, logs, complex numbers and every CATALOG command.
App 2
Statistics
1- and 2-variable statistics and seven regression models, with a data-entry table and a full set of summary results.
Statistics
❶1-Variable
❷y=a+bx
❸y=a+bx+cx²
App 3
Table
Generates a table of values from one or two functions, f(x) and g(x), over a start/end/step range.
App 4
Equation
Solves simultaneous linear equations (2 to 4 unknowns) and polynomial equations (quadratic, cubic, quartic).
Equation
❶Simult. Equation
❷Polynomial
App 5
Inequality
Solves quadratic, cubic and quartic inequalities and reports the solution intervals.
Inequality
❶Order 2 (ax²…)
❷Order 3
❸Order 4
App 6
Distribution
Normal, Binomial and Poisson probability — both probability density (PD) and cumulative distribution (CD).
Distribution
❶Normal PD
❷Normal CD
❸Binomial PD
App 7
Complex
Dedicated complex-number arithmetic with rectangular (a + bi) and polar (r∠θ) results.
App 8
Matrix
Matrix arithmetic up to 4×4 — addition, subtraction, multiplication, determinant, inverse and transpose.
Matrix
❶Define MatA
❷Define MatB
❸MatA + MatB
App 9
Vector
2D and 3D vector operations — dot product, cross product, magnitude, angle and unit vectors.
Vector
❶Define VctA
❷Define VctB
❸VctA · VctB
App 10
Spreadsheet
A 5-column (A–E) × 45-row spreadsheet with cell formulas, fill/copy tools and range functions (Sum, Min, Max, Mean).
App 11
Ratio
Solves proportions of the form a : b = c : x for the unknown term.
Ratio
❶a:b = c:x
❷a:b = x:d
App 12
Math Box
Probability and learning tools — dice roll, coin toss, number line and circle simulations.
Math Box
❶Dice Roll
❷Coin Toss
❸Number Line
App 13
Base-N
Binary, octal, decimal and hexadecimal calculations with logic operators (and, or, xor, not).
Extended Display & Explainer
The Extended DisplayPresentation mode
When teaching with the SC-991BF on a large screen, open the extended display with the ⧉ (cast) button in the title bar. A greatly enlarged copy of the calculator’s LCD appears beside the keypad so the whole class can read the current expression and result. The panel is marked LIVE DISPLAY and refreshes automatically as you type.
Use the size controls (− % +) to fit the calculator to any display, and press HIDE to collapse the panel. The extended display always mirrors exactly what is on the calculator’s own screen.
The ExplainerEXPLANATION & STEPS
Below the extended display, the explainer turns any Calculate result into a lesson. It has two tabs:
- EXPLANATION — a plain-language walkthrough of what each function and operation does, in order.
- STEPS — the working shown as a reduction: the expression is rewritten one step at a time, each line a little more simplified, down to the final answer (shown in green).
NoteThe explainer is available in the Calculate app for any expression you evaluate. Both the wording and the step chain are produced by the calculator itself — they always match the actual computation.
Example 1 — roots and arithmetic
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
Math DEG
2×√(2)+3
5.8284271248
EXPLANATIONSTEPS
EXPLANATION
A square root asks: which number, multiplied by itself, gives 2? Since 1.4142135624 × 1.4142135624 = 2, we get √2 = 1.4142135624.
Multiply 2 by 1.4142135624: 2 × 1.4142135624 = 2.8284271248.
Add 2.8284271248 and 3 together: 2.8284271248 + 3 = 5.8284271248.
STEPS
2×√(2)+3
√2 = 1.4142135624
= 2 × 1.4142135624 = 2.8284271248
= 2.8284271248 + 3 = 5.8284271248
Example 2 — trigonometry (Degree)
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
EXPLANATIONSTEPS
EXPLANATION
sin gives sine of the angle. Here sin(30°) = 0.5.
cos gives cosine of the angle. Here cos(60°) = 0.5.
Add 0.5 and 0.5 together: 0.5 + 0.5 = 1.
STEPS
sin(30)+cos(60)
sin(30°) = 0.5
= cos(60°) = 0.5
= 0.5 + 0.5 = 1
Example 3 — powers
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
EXPLANATIONSTEPS
EXPLANATION
Squaring means multiplying a number by itself. So 3² = 3 × 3 = 9.
Squaring means multiplying a number by itself. So 4² = 4 × 4 = 16.
Add 9 and 16 together: 9 + 16 = 25.
STEPS
3^2+4^2
3² = 9
= 4² = 16
= 9 + 16 = 25
Example 4 — logarithms
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
EXPLANATIONSTEPS
EXPLANATION
log gives logarithm (base 10). Here log(1,000) = 3.
ln gives natural logarithm (base e). Here ln(1) = 0.
Add 3 and 0 together: 3 + 0 = 3.
STEPS
log(1000)+ln(1)
log(1,000) = 3
= ln(1) = 0
= 3 + 0 = 3
Example 5 — implicit multiplication priority
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
EXPLANATIONSTEPS
EXPLANATION
Divide 6 by 2 — splitting 6 into 2 equal parts: 6 ÷ 2 = 3.
Add 1 and 2 together: 1 + 2 = 3.
Multiply 3 by 3 (writing them side by side means multiply): 3 × 3 = 1.
STEPS
6÷2(1+2)
6 ÷ 2 = 3
= 1 + 2 = 3
= 3 × 3 = 1
Example 6 — order of operations
eBidyaloy · EXTENDED DISPLAYLIVE DISPLAY
EXPLANATIONSTEPS
EXPLANATION
Multiply 3 by 4: 3 × 4 = 12.
Add 7 and 12 together: 7 + 12 = 19.
Subtract 2 from 19: 19 − 2 = 17.
STEPS
7+3×4−2
3 × 4 = 12
= 7 + 12 = 19
= 19 − 2 = 17
Calculate App Reference
CalculateGeneral & scientific calculation
The Calculate app is the calculator's main workspace. Enter an expression in natural textbook format and press EXE to evaluate it. This chapter covers every function available in Calculate, grouped by type, each with a worked example.
NoteUnless a note says otherwise, examples assume the default settings — Angle Unit: Degree, and MathI/MathO input/output.
Basic Arithmetic & Priority
Use + − × ÷ for the four operations and ( ) to group terms. Calculations follow standard priority: functions and powers first, then × ÷, then + −. An omitted × (implicit multiplication) before a bracket or constant binds tighter than ÷.
Example 1To calculate 7 × 8 − 4 × 5
7 × 8 − 4 × 5 EXE
Multiplication is done before subtraction: 56 − 20 = 36.
Example 2To calculate 6 ÷ 2(1 + 2)
6 ÷ 2 ( 1 + 2 ) EXE
Implicit multiplication binds tighter than ÷, so this reads 6 ÷ (2 × (1 + 2)) = 6 ÷ 6 = 1.
Fractions
Press ▢∕▢ for a fraction template and SHIFT ▢∕▢ for a mixed number. Results appear as fractions; press ⇄ (FORMAT) to switch to a decimal.
Example 3To calculate 3⁄4 + 1⁄6
3 ▢∕▢ 4 ▶ + 1 ▢∕▢ 6 EXE
Math DEG
3⁄4 + 1⁄6
0.9166666667
The exact result is shown as the fraction 11⁄12. Press ⇄ to see it as the decimal 0.9166666667.
Powers & Roots
▢² squares, SHIFT ▢² cubes, ▢^ raises to any power, √▢ is a square root, SHIFT √▢ a cube root, and SHIFT ▢^ gives the x-th root.
Example 4To calculate 5² + 12²
5 ▢² + 1 2 ▢² EXE
25 + 144 = 169. (Its square root, 13, is the hypotenuse of a 5-12-13 triangle.)
Example 5To calculate the 5th root of 32
SHIFT ▢^ 5 ▶ 3 2 EXE
The x-th root key gives ⁵√32 = 2, because 2⁵ = 32.
Exponential & Logarithmic
log is base-10 log, ln is natural log, SHIFT log is 10ˣ, SHIFT ln is eˣ. Use the CATALOG log▢(▢) for a logarithm to any base.
Example 6To calculate log 1000
log 1 0 0 0 ) EXE
log 1000 = 3, because 10³ = 1000.
Example 7To calculate log₂ 32 (log to base 2)
CATALOG log▢(▢) → 2, 32 → EXE
Enter the base in the small box: log₂ 32 = 5, because 2⁵ = 32.
Trigonometric Functions
sin cos tan and their inverses (SHIFT + the key) use the current Angle Unit. Append ° ʳ ᵍ (from CATALOG) to give a value in a specific unit regardless of the mode.
Example 8To calculate sin 30° (Degree mode)
sin 3 0 ) EXE
In Degree mode sin 30° = 0.5.
Example 9To calculate tan⁻¹ 1 (Degree mode)
SHIFT tan 1 ) EXE
The inverse tangent of 1 is the angle whose tangent is 1: 45°.
Hyperbolic Functions
The hyperbolic functions sinh, cosh, tanh and their inverses are on the CATALOG menu.
Example 10To calculate sinh 1
CATALOG sinh 1 ) EXE
Math DEG
sinh 1
1.1752011936
sinh 1 = (e − e⁻¹) / 2 ≈ 1.1752.
Percentage
Enter a value followed by SHIFT ( (the % operator). A percentage is interpreted as “per hundred”.
Example 11To calculate 150 × 20%
1 5 0 × 2 0 SHIFT ( EXE
20% of 150 is 30.
Permutation, Combination & Factorial
SHIFT × is nPr, SHIFT ÷ is nCr, and x! (factorial) is on the CATALOG menu.
Example 12To calculate 5 P 2 (permutations)
5 SHIFT × 2 EXE
The number of ordered arrangements of 2 from 5 is 20.
Example 13To calculate 8 C 3 (combinations)
8 SHIFT ÷ 3 EXE
The number of unordered selections of 3 from 8 is 56.
Numeric Functions
The CATALOG provides Abs (absolute value), Int (truncate), Frac (fractional part), Intg (floor), Rnd (round to the display) and x⁻¹ (reciprocal).
Example 14To calculate |2 − 7| (absolute value)
FUNCTION Abs 2 − 7 ) EXE
The absolute value strips the sign: |−5| = 5.
GCD, LCM & Random
From the CATALOG: GCD(, LCM(, RanInt#( (a random integer in a range) and Ran# (a random number in [0, 1)).
Example 15To calculate GCD(48, 36)
CATALOG GCD( 48, 36 → EXE
The greatest common divisor of 48 and 36 is 12.
Example 16To calculate LCM(6, 8)
CATALOG LCM( 6, 8 → EXE
The least common multiple of 6 and 8 is 24.
Calculus — Derivative & Integral
The CATALOG offers d/dx (numerical derivative at a point) and ∫dx (definite integral between limits).
Example 17To calculate d/dx(x²) at x = 3
CATALOG d/dx → x², at 3 → EXE
The slope of x² at x = 3 is 2x = 6.
Example 18To calculate ∫ x² dx from 0 to 1
CATALOG ∫dx → x², 0, 1 → EXE
Math DEG
∫₀¹ x² dx
0.3333333333
The area under x² from 0 to 1 is 1⁄3 ≈ 0.3333.
Summation & Product
Σ sums and Π multiplies an expression as a counter runs from a lower to an upper limit.
Example 19To calculate Σ x for x = 1 to 10
CATALOG Σ → x, 1, 10 → EXE
1 + 2 + … + 10 = 55.
Example 20To calculate Π x for x = 1 to 5
CATALOG Π → x, 1, 5 → EXE
1 × 2 × 3 × 4 × 5 = 5! = 120.
SOLVE, CALC & VERIFY
SOLVE finds a root of f(x) = 0 by Newton's method. CALC evaluates an expression after prompting for each variable. VERIFY tests whether a relation (=, ≠, <, >, ≤, ≥) is true.
Example 21SOLVE — a root of x² − 4 = 0
x ▢² − 4 CATALOG SOLVE EXE
SOLVE searches from the stored x and finds the nearby root x = 2.
Example 22CALC — evaluate 2A + B with A = 3, B = 4
2 VARIABLE A + VARIABLE B CATALOG CALC
CALC prompts for A then B, then evaluates 2·3 + 4 = 10.
Example 23VERIFY — is 3 × 4 = 12 ?
3 × 4 CATALOG VERIFY = 12 EXE
VERIFY confirms the relation is True.
Coordinate Conversion
Pol( converts rectangular (x, y) to polar (r, θ); Rec( converts polar (r, θ) back to rectangular (x, y). Both are on the CATALOG.
Example 24Pol( — convert (3, 4) to polar
CATALOG Pol( 3, 4 → EXE
Math DEG
Pol(3, 4)
r = 5, θ = 53.13°
The point (3, 4) has magnitude r = 5 and angle θ = 53.13° (Degree mode).
Example 25Rec( — convert (2, 60°) to rectangular
CATALOG Rec( 2, 60 → EXE
Math DEG
Rec(2, 60°)
x = 1, y = 1.732
The polar point r = 2, θ = 60° becomes (1, 1.732).
Variables, Ans & Constants
Store a result into A–F, x, y, z or M with the VARIABLE menu, and recall it later. Ans reuses the previous answer; SHIFT 7/8 insert π and e. Physical constants come from CATALOG → CONST ▸.
Example 26To calculate π × 2
SHIFT 7 × 2 EXE
Math DEG
π × 2
6.2831853072
π × 2 ≈ 6.2832. Press ⇄ to keep the exact form 2π.
Example 27To store 5 in A, then compute A × 3
5 VARIABLE A ▸ Store … VARIABLE A × 3 EXE
Recalling the stored variable A gives 5 × 3 = 15.
Result Formats & Tools
After a result, ⇄ (FORMAT / S⇔D) toggles exact ⇄ decimal, and the TOOLS menu offers Prime Factor, Recurring Decimal, Sexagesimal and Improper Fraction. The CATALOG adds ENG (engineering form) and FACT.
Example 28S⇔D — toggle √8 between exact and decimal
√ 8 ) EXE ⇄
Math DEG
√8
2√2 ⇄ 2.8284271248
The exact form 2√2 and the decimal 2.8284… are the same value shown two ways.
Example 29FACT — prime-factorise 360
3 6 0 EXE CATALOG FACT
FACT breaks a whole number into its prime factors.
Example 30ENG — engineering notation for 12345
1 2 3 4 5 EXE CATALOG ENG
Math DEG
12345
12.345 × 10³
ENG shifts the exponent to a multiple of 3, ready for SI prefixes.
Statistics App Reference
Statistics1-variable & 2-variable analysis
The Statistics app summarises a set of data and fits regression models. You type values into a list, then read off statistics such as the mean, standard deviation and quartiles; for paired data it also finds the line or curve of best fit. Open it from HOME by pointing to Statistics and pressing OK.
Choosing an analysis type
Select Calculation
11-Variable
2y = a + bx
3y = a + bx + cx²
4y = a + b·ln(x)
5y = a·e^(bx)
Choose 1-Variable for a single list of numbers, or one of the 2-Variable regression models for paired (x, y) data. The list continues with y = a·bx, y = a·xb and y = a + b/x. Changing the type later clears the data.
Entering data
Type a value and press EXE to drop to the next row. Move with the arrow keys, overwrite a cell by typing over it, and delete a value with DEL. To weight values by how often they occur, turn on the Frequency column from ⚙ → Statistics ▸ Frequency ▸ On.
1-Variable statistics
Example 1To summarise the data 2, 5, 6, 8, 9
Statistics ▸ 1-Variable → enter data → FUNCTION
1-Variable Result
x̄6
Σx30
Σx²210
σₓ2.4494897428
sₓ2.7386127875
The mean is x̄ = Σx / n = 30 / 5 = 6. Two standard deviations are reported: σₓ (population, ÷ n) and sₓ (sample, ÷ n − 1).
Enter the data with:
2›EXE›5›EXE›6›EXE›8›EXE›9›EXE›FUNCTION
Example 2To read the order statistics (same data)
scroll the result with ▼
1-Variable Result (2/2)
minX2
Q₁3.5
Median6
Q₃8.5
maxX9
Scrolling down shows the five-number summary: minimum 2, first quartile 3.5, median 6, third quartile 8.5 and maximum 9.
Noteσ (divide by n) treats the data as the whole population; s (divide by n − 1) treats it as a sample estimating a larger population. Both are always shown.
Example 3To weight values with a frequency column
⚙ Frequency ▸ On → enter x and Freq
Here the value 10 occurs twice, 20 five times and 30 three times (n = 10 in total), giving x̄ = 21, σₓ = 7 and sₓ = 7.3786….
Normal distribution from 1-variable data
On the 1-variable result screen, press EXE to open the Norm-Dist tools. They convert a data value x to a probability using the fitted mean and σ: P(t) is the lower-tail area Φ(t), Q(t) = Φ(t) − 0.5, R(t) = 1 − Φ(t), and ▸t standardises x into t = (x − x̄) / σₓ.
Example 4To standardise x = 8 and read its probability
1-Variable Result → EXE → ▸t / P(
Norm-Dist
▸t (x=8)0.8164965809
P(t)0.792891967
Q(t)0.292891967
R(t)0.207108033
The value 8 standardises to t = (8 − 6) / 2.449 = 0.8165, and about 79.3% of a normal population lies below it (P(t)).
Two-variable regression
Choose a 2-variable model to get an x and a y column. Enter each pair, then press FUNCTION for the fitted coefficients and the correlation r.
Example 5To fit a line to (1,3) (2,5) (3,7) (4,8) (5,11)
Statistics ▸ y = a + bx → enter pairs → FUNCTION
Regression Result
a1.1
b1.9
r0.9904434668
x̄3
ȳ6.8
The line of best fit is y = 1.1 + 1.9x and the correlation r = 0.990 shows a strong positive relationship.
Example 6To estimate ŷ and x̂ from the fitted line
VARIABLE ▸ ŷ / x̂
Estimated Values
ŷ (x = 6)12.5
x̂ (y = 9)4.1578947368
Type a value then the estimate function: ŷ predicts y on the line at x = 6 (12.5); x̂ solves the line for x when y = 9.
Example 7To fit an exponential model y = a·e^(bx)
Statistics ▸ y = a·e^(bx) → (1,2)(2,4)(3,8)(4,16) → FUNCTION
Exp Regression
a1
b0.6931471806
r1
The data doubles each step, so the fit is y = 1·e^(0.6931x) — and e^0.6931 = 2 exactly. Non-linear models drop any point that transforms to an undefined value.
| Menu item | Model | Reports r? |
| y = a + bx | Linear | Yes |
| y = a + bx + cx² | Quadratic | No (a, b, c) |
| y = a + b·ln(x) | Logarithmic | Yes |
| y = a·ebx | e Exponential | Yes |
| y = a·bx | ab Exponential | Yes |
| y = a·xb | Power | Yes |
| y = a + b/x | Inverse | Yes |
Statistics calculation screen
Example 8To combine statistics in an expression (x̄ × 2 + Σx)
TOOLS ▸ Stat-Calc → VARIABLE inserts x̄, Σx …
Press TOOLS on a result screen for a free-form editor. Using the 1-variable data (x̄ = 6, Σx = 30): x̄ × 2 + Σx = 12 + 30 = 42. Any statistic can be reused this way.
Distribution App Reference
DistributionNormal, Binomial & Poisson
The Distribution app evaluates the common probability distributions. Choose a distribution from the menu, enter its parameters, and read the probability — or, for the list distributions, a whole table of probabilities.
Choosing a distribution
Distribution
1Normal PD
2Normal CD
3Inverse Normal
4Binomial PD
5Binomial CD
PD gives the density / mass at a point; CD gives the cumulative probability up to a bound. The list also has Poisson PD and Poisson CD.
Normal distribution
Example 1Normal PD — density f(x) at x = 0.5, μ = 0, σ = 1
Distribution ▸ Normal PD → x, μ, σ → EXE
Normal PD
x0.5
μ0
σ1
f(x)0.3520653268
f(x) is the height of the bell curve, not a probability. For the standard normal the height at x = 0.5 is 0.3521.
Example 2Normal CD — P(−1 ≤ X ≤ 1) for μ = 0, σ = 1
Distribution ▸ Normal CD → Lower, Upper, μ, σ → EXE
Normal CD
Lower−1
Upper1
P0.6826894723
The area between the bounds is the probability. This is the classic “68% within one σ”.
Example 3Normal CD — heights ~N(170, 6), P(160 ≤ X ≤ 180)
Normal CD → 160, 180, 170, 6 → EXE
Normal CD
Lower160
Upper180
μ170
σ6
P0.9044193359
About 90.4% of this population lies between 160 and 180 cm. For a one-sided probability use a very large or very small bound (e.g. Lower = −1×10⁹⁹).
Example 4Inverse Normal — the value with 97.5% below it
Distribution ▸ Inverse Normal → Area, μ, σ → EXE
Inverse Normal
Area0.975
μ0
σ1
xInv1.9599639861
Inverse Normal reverses the question. The value with 97.5% of the standard-normal area below it is 1.96 — the familiar 95%-confidence cut-off.
Binomial distribution (list input)
Enter N (trials) and p (success probability) once, then a growable list of x values; a probability is returned for each. PD gives P(X = x); CD gives P(X ≤ x).
Example 5Binomial PD — N = 10, p = 0.5, for x = 0…4
Distribution ▸ Binomial PD → N=10, p=0.5, x-list → EXE
Binomial PD
| x | P |
|---|
| 0 | 0.0009765625 |
| 1 | 0.009765625 |
| 2 | 0.0439453125 |
| 3 | 0.1171875 |
| 4 | 0.205078125 |
Ten fair coin tosses: the probability of exactly 3 heads is 0.1172. Add as many x values as you like to build the whole table.
Example 6Binomial CD — P(X ≤ 3), N = 10, p = 0.5
Binomial CD → N=10, p=0.5, x=3 → EXE
The cumulative form adds P(X = 0…3) = 0.171875 — the chance of at most 3 heads.
Poisson distribution (list input)
Example 7Poisson PD — λ = 3, for x = 0…4
Distribution ▸ Poisson PD → λ=3, x-list → EXE
Poisson PD
| x | P |
|---|
| 0 | 0.0497870684 |
| 1 | 0.1493612051 |
| 2 | 0.2240418077 |
| 3 | 0.2240418077 |
| 4 | 0.1680313557 |
Events at an average rate λ = 3. The most likely counts are 2 and 3, each with probability 0.2240.
Example 8Poisson CD — P(X ≤ 2), λ = 3
Poisson CD → λ=3, x=2 → EXE
Adding P(X = 0, 1, 2) gives 0.4232 — the chance of two or fewer events.
Important!List distributions accept several x values at once — add rows to the x list and every row is evaluated, giving a probability table you can scroll.
Table App Reference
TableFunction value tables
The Table app tabulates one or two functions over a range of x — ideal for plotting points, spotting where a function crosses zero, and comparing two functions side by side.
Defining the function(s) and range
Type the formula for f(x) using the x key for the variable. To tabulate a second function, turn on g(x) from ⚙ → Table ▸ f(x)/g(x). The calculator then asks for Start, End and Step and builds a row for each x (up to 45 rows).
Example 1To tabulate f(x) = x² − 3 for x = 1 … 5
Table → f(x) = x² − 3 → Start 1, End 5, Step 1 → EXE
Between x = 1 and x = 2 the value changes sign (−2 → 1), so the graph crosses zero there — a quick way to locate a root. Scroll with ▲ ▼.
Enter the function with:
x›x²›−›3›EXE›1›EXE›5›EXE›1›EXE
Example 2To tabulate f(x) = x² − 3 and g(x) = 2x + 1 together
⚙ f(x)/g(x) ▸ On → g(x) = 2x + 1 → x = 1 … 4
The two columns are closest near x = 3 (6 vs 7), showing roughly where the curves x² − 3 and 2x + 1 intersect.
NoteThe table holds up to 45 rows. If Start, End and Step would produce more, the list is truncated to fit. Edit the function or range from the ⚙ menu and the table regenerates.
Equation App Reference
EquationSimultaneous systems & polynomials
The Equation app solves two kinds of problem: simultaneous linear systems with 2, 3 or 4 unknowns, and polynomial equations of degree 2, 3 or 4. You enter only the coefficients and the calculator returns the complete solution set.
Choosing an equation type
Equation Type
1Simultaneous · 2 unknowns
2Simultaneous · 3 unknowns
3Simultaneous · 4 unknowns
4Polynomial · ax²+bx+c
5Polynomial · ax³+…
The list ends with Polynomial · ax⁴+bx³+cx²+dx+e. Point to a type and press OK; the calculator lays out exactly the coefficient boxes that type needs.
Simultaneous equations
Each row of the grid is one equation. For 2 unknowns the columns are x, y and the constant =. Enter the coefficients left to right, pressing EXE after each.
Example 1To solve 2x + 3y = 8 and x − y = −1
Equation ▸ Simultaneous · 2 unknowns → coefficients → EXE
Enter the two rows (2, 3, 8) and (1, −1, −1). The unique solution is x = 1, y = 2.
Key operation:
2›EXE›3›EXE›8›EXE›1›EXE›(−)›1›EXE›(−)›1›EXE
Example 2To solve a 3-unknown system
Equation ▸ Simultaneous · 3 unknowns → EXE
For x + y + z = 6, x − y + 2z = 5 and 2x + y − z = 1 the solution is x = 1, y = 2, z = 3. A 4-unknown system adds a w column.
NoteIf a system has no unique solution the calculator reports Infinite Solutions or No Solution instead of values.
Polynomial equations
Enter the coefficients from the highest power down. The quadratic x² − 5x + 6 = 0 uses a = 1, b = −5, c = 6.
Example 3To solve the quadratic x² − 5x + 6 = 0
Equation ▸ Polynomial · ax²+bx+c → 1, −5, 6 → EXE
The two roots are x = 3 and x = 2. After solving a quadratic or cubic, the result screen also offers the minimum / maximum point (vertex) of the curve.
Example 4To solve the cubic x³ − 6x² + 11x − 6 = 0
Polynomial · ax³+… → 1, −6, 11, −6 → EXE
Three real roots: 1, 2 and 3.
Example 5To solve the quartic x⁴ − 5x² + 4 = 0
Polynomial · ax⁴+… → 1, 0, −5, 0, 4 → EXE
Quartic Roots
x₁2
x₂1
x₃−1
x₄−2
Four real roots: ±1 and ±2. Enter 0 for any missing power (here b and d are 0).
Complex roots
When a polynomial has non-real roots, the Equation Complex Roots setting decides whether they are shown. It is Off by default (only real roots appear). Turn it on from SETTINGS → Equation Complex Roots ▸ On.
Example 6To show the complex roots of x² + 2x + 5 = 0
SETTINGS ▸ Equation Complex Roots ▸ On → solve
Complex Roots
x₁−1 + 2i
x₂−1 − 2i
This equation has no real roots. With the setting on it returns the conjugate pair −1 ± 2i; with it off it reports No Real Roots.
Inequality App Reference
InequalityPolynomial inequalities
The Inequality app solves a polynomial inequality and reports the solution as a set of intervals on the number line. It handles quadratic, cubic and quartic inequalities against 0.
Choosing degree and direction
Inequality Degree
1Quadratic ax²+bx+c
2Cubic ax³+bx²+cx+d
3Quartic ax⁴+…+e
After the degree, choose the direction against zero — > 0, < 0, ≥ 0 or ≤ 0 — then enter the coefficients exactly as in the Equation app.
Example 1To solve x² − 5x + 6 > 0
Inequality ▸ Quadratic ▸ > 0 → 1, −5, 6 → EXE
Ineq DEG
x² − 5x + 6 > 0
x < 2 or x > 3
The factors are (x − 2)(x − 3), so the expression is positive outside the roots: x < 2 or x > 3.
Example 2To solve x² − 5x + 6 ≤ 0
Quadratic ▸ ≤ 0 → 1, −5, 6 → EXE
Ineq DEG
x² − 5x + 6 ≤ 0
2 ≤ x ≤ 3
With ≤, the boundary roots are included, so the answer is the closed interval 2 ≤ x ≤ 3. The app writes ≤ / ≥ for inclusive directions and < / > for strict ones.
Example 3To solve x³ − x > 0
Cubic ▸ > 0 → 1, 0, −1, 0 → EXE
Ineq DEG
x³ − x > 0
−1 < x < 0 or x > 1
The roots are −1, 0 and 1; testing each region gives two solution intervals, joined with “or”.
NoteIf the inequality is true everywhere the app shows All Real Numbers; if it is never true it shows No Solution.
Complex App Reference
ComplexArithmetic with complex numbers
The Complex app performs the four operations on two complex numbers z₁ = a + bi and z₂ = c + di, and can show the result in rectangular (a + bi) or polar (r∠θ) form. The imaginary unit i satisfies i² = −1.
Selecting the operation
Operation
1z₁ + z₂
2z₁ − z₂
3z₁ × z₂
4z₁ ÷ z₂
Pick the operation first, then enter the real and imaginary parts of each number into the coefficient grid. The examples below all use z₁ = 3 + 2i and z₂ = 1 + 4i.
Example 1To add (3 + 2i) + (1 + 4i)
Complex ▸ z₁ + z₂ → 3, 2, 1, 4 → EXE
Add the real parts and the imaginary parts separately: (3 + 1) + (2 + 4)i = 4 + 6i.
Example 2To subtract (3 + 2i) − (1 + 4i)
z₁ − z₂ → EXE
Subtract componentwise: (3 − 1) + (2 − 4)i = 2 − 2i.
Example 3To multiply (3 + 2i) × (1 + 4i)
z₁ × z₂ → EXE
Use the distributive law with i² = −1: (3·1 − 2·4) + (3·4 + 2·1)i =
−5 + 14i. Enter it with
3›EXE›2›EXE›1›EXE›4›EXE›FUNCTION
Example 4To divide (3 + 2i) ÷ (1 + 4i)
z₁ ÷ z₂ → EXE
Result
z₁ ÷ z₂0.6470588235 − 0.5882352941i
Multiply top and bottom by the conjugate of the denominator (1 − 4i). The denominator becomes 1² + 4² = 17, a real number.
Polar form and complex functions
Set Complex Result ▸ r∠θ in SETTINGS to read a result in polar form. The FUNCTION menu inside the app also offers Abs (modulus |z|), arg (argument), Conjg (conjugate z̄), ReP (real part) and ImP (imaginary part).
Example 5To read 1 + i in polar form
SETTINGS ▸ Complex Result ▸ r∠θ
Polar (Deg)
1 + i√2 ∠ 45°
|1 + i|1.4142135624
arg(1 + i)45
1 + i has modulus r = √2 ≈ 1.4142 and argument θ = 45° (in Degree mode). Changing the Angle Unit changes how θ is reported.
NoteConjg flips the sign of the imaginary part (a + bi → a − bi); ReP and ImP extract the real and imaginary components as ordinary numbers.
Base-N App Reference
Base-NBinary, octal, decimal & hexadecimal
The Base-N app works with whole numbers in four bases — DEC (10), HEX (16), OCT (8) and BIN (2) — and includes the bitwise logic operators. All arithmetic is integer arithmetic on a 32-bit two's-complement value.
Switching base
The active base is shown at the top of the screen. Press the base soft keys DEC, HEX, OCT, BIN to re-display the current value in another base — the value never changes, only its notation.
Example 1To view the number 250 in every base
Base-N → 250 → HEX / OCT / BIN
250 in every base
| Base | Value |
|---|
| DEC | 250 |
| HEX | FA |
| OCT | 372 |
| BIN | 11111010 |
Enter 250 in DEC, then tap each base key. The single quantity 250 is FA in hexadecimal, 372 in octal and 11111010 in binary.
Example 2To convert hexadecimal FF to decimal
Base-N ▸ HEX → FF → DEC
Type FF while the base is HEX (digits A–F appear on the number keys), then switch to DEC to read 255.
Bitwise logic operators
Press CATALOG in Base-N to insert a logic operator: and, or, xor, xnor, not and Neg (two's-complement negate). These operate on the binary bit patterns.
Example 31100 and 1010 (in binary)
BIN → 1100 and 1010 → EXE
Base BIN
1100 and 1010
1000
and keeps bits that are set in BOTH operands: only the leading bit is set in both, so the result is 1000.
Example 41100 or 1010 (in binary)
BIN → 1100 or 1010 → EXE
or keeps bits set in EITHER operand, giving 1110.
Negative values
Decimal shows a signed value; the other bases show the 32-bit two's-complement bit pattern, so a negative number prints as its unsigned pattern.
Example 5To view −5 in two's-complement form
Base-N → −5 → HEX / BIN
−5 in two's complement
| Base | Value |
|---|
| DEC | −5 |
| HEX | FFFFFFFB |
| BIN | …11111011 |
In DEC, −5 keeps its sign. In HEX it is FFFFFFFB, and in BIN the full 32-bit pattern ends in …11111011.
Important!Base-N is integer-only: fractions, decimals and roots are not available, and a result outside the signed 32-bit range (−2 147 483 648 … 2 147 483 647) is a Math ERROR.
Matrix App Reference
MatrixMatrix arithmetic up to 4×4
The Matrix app performs calculations with matrices of up to four rows and four columns (and rectangular m×n matrices). You store values in the matrix memories MatA, MatB, MatC and MatD, then build an expression from them. The result of every matrix calculation is retained in a special memory called MatAns, which you can feed straight into the next calculation.
Creating and entering a matrix
When you open an operation, the calculator first asks for the dimensions (rows × columns), then shows an empty grid. Fill it cell by cell, pressing EXE after each value to advance to the next cell. This grid holds MatA = 2111:
Choose 2 rows and 2 columns, then key in the four values:
2›EXE›1›EXE›1›EXE›1›EXE
Important!A matrix memory keeps its contents until you overwrite it or clear the app, so you can reuse MatA in several calculations without re-entering it.
The examples below all use these four matrices:
MatA = 2111 MatB = 2321 MatC = 10−10−11 MatD = 123456789
Addition and Subtraction
Example 1To add two matrices (MatA + MatB)
Matrix ▸ MatA + MatB → enter MatA, MatB → EXE
Corresponding entries are added: the (1,1) entries 2 + 2 = 4, the (1,2) entries 1 + 3 = 4, and so on, giving 4432.
Example 2To subtract two matrices (MatA − MatB)
Matrix ▸ MatA − MatB → enter MatA, MatB → EXE
Subtraction is also entry by entry: 2 − 2 = 0, 1 − 3 = −2, and so on.
NoteThe two matrices must have the same dimensions in order to be added or subtracted. An error occurs if you try to add or subtract matrices of different dimensions.
Multiplication
Example 3To multiply two matrices (MatA × MatB)
Matrix ▸ MatA × MatB → enter MatA, MatB → EXE
Each result entry is a row × column dot product. The (1,1) entry is (row 1 of MatA)·(column 1 of MatB) = 2·2 + 1·2 = 6; the (1,2) entry is 2·3 + 1·1 = 7.
Example 4To multiply matrices of different sizes (MatA × MatC)
Matrix ▸ MatA × MatB → MatA (2×2), MatC (2×3) → EXE
A 2×2 times a 2×3 gives a 2×3 result, because MatA has 2 columns and MatC has 2 rows.
Important!Matrix multiplication is only possible when the number of columns of the left matrix equals the number of rows of the right matrix. Note that MatA × MatB and MatB × MatA are generally not the same.
Powers — Square and Cube
A square matrix can be raised to a power. MatA² means MatA × MatA, and MatA³ means MatA × MatA × MatA.
Example 5To square and cube MatA (MatA², MatA³)
Matrix ▸ MatA² / MatA³ → EXE
MatA² = 5332. Cubing goes one step further: MatA³ = MatA² × MatA = 13885.
Inverse
The inverse MatA⁻¹ is the matrix that satisfies MatA × MatA⁻¹ = I (the identity). It exists only for a square matrix whose determinant is non-zero.
a₁₁−1 = 1a₁₁
a₁₁a₁₂a₂₁a₂₂−1 = a₂₂−a₁₂−a₂₁a₁₁a₁₁a₂₂ − a₁₂a₂₁
Example 6To invert MatA (MatA⁻¹)
Matrix ▸ MatA det / inv / trans ▸ Inverse Matrix → EXE
Because det(MatA) = 1, the inverse is 1−1−12. You can check it: MatA × MatA⁻¹ returns the identity matrix.
Note- Only square matrices (same number of rows and columns) can be inverted. Trying to invert a matrix that is not square produces an error.
- A matrix with a determinant of zero cannot be inverted — for example MatD above has det 0, so MatD⁻¹ is an error.
- Calculation precision is affected for matrices whose determinant is near zero.
Determinant
The determinant is a single number describing a square matrix. For 1×1, 2×2 and 3×3 matrices it is computed as:
det a₁₁ = a₁₁
det a₁₁a₁₂a₂₁a₂₂ = a₁₁a₂₂ − a₁₂a₂₁
det a₁₁a₁₂a₁₃a₂₁a₂₂a₂₃a₃₁a₃₂a₃₃ = a₁₁a₂₂a₃₃ + a₁₂a₂₃a₃₁ + a₁₃a₂₁a₃₂ − a₁₃a₂₂a₃₁ − a₁₂a₂₁a₃₃ − a₁₁a₂₃a₃₂
Example 7To obtain the determinant of MatA (Det(MatA))
Matrix ▸ MatA det / inv / trans ▸ Determinant → EXE
det(MatA) = a₁₁a₂₂ − a₁₂a₂₁ = 2·1 − 1·1 = 1. A determinant is a scalar, so the result is a single value.
NoteDeterminants can be obtained only for square matrices. Trying to obtain a determinant for a non-square matrix produces an error. The determinant of MatD (above) is 0, which is why it has no inverse.
Transpose
The transpose Mᵀ turns rows into columns. It works for any matrix, including rectangular ones.
Example 8To transpose MatC (Trn(MatC))
Matrix ▸ MatA det / inv / trans ▸ Transpose → MatC → EXE
The 2×3 matrix MatC becomes a 3×2 matrix — row 1 (1, 0, −1) becomes column 1, and row 2 (0, −1, 1) becomes column 2.
Identity Matrix
Identity(n) creates the n×n identity matrix — 1s on the main diagonal and 0s everywhere else. Multiplying any matrix by the identity leaves it unchanged.
Example 9To create the 3×3 identity matrix (Identity(3))
Matrix ▸ Identity(n) → 3 → EXE
Enter the size n = 3. Larger results that overflow the screen can be scrolled with the ▲ ▼ ◀ ▶ keys.
NoteThe result of each matrix calculation is stored in MatAns. You can use MatAns in a following calculation — for example, invert a matrix and then multiply the original by MatAns to confirm you get the identity.
Vector App Reference
Vector2D & 3D vector operations
The Vector app stores two vectors, VctA and VctB, in 2 or 3 dimensions and computes their sum, difference, dot product, cross product, magnitudes, the angle between them and their unit vectors.
Choosing dimensions
Vector Dimension
12D vectors (x, y)
23D vectors (x, y, z)
Pick 2D or 3D, then enter the components of VctA and VctB. The 2D cross product is a single scalar; the 3D cross product is another vector.
A · B = AxBx + AyBy + AzBz |A| = √(Ax² + Ay² + Az²) cos θ = A · B|A| |B|
Example 13D vectors VctA = (1, 2, 3), VctB = (4, 5, 6)
Vector ▸ 3D vectors → enter A, B → FUNCTION
Vector Result (Deg)
VctA · VctB32
VctA × VctB(−3, 6, −3)
|VctA|3.7416573868
Angle12.9331544919
The dot product is 1·4 + 2·5 + 3·6 = 32; the cross product (−3, 6, −3) is perpendicular to both; |VctA| = √14 ≈ 3.742; and the angle is about 12.93° (Degree mode).
Key operation:
1›EXE›2›EXE›3›EXE›4›EXE›5›EXE›6›EXE›FUNCTION
Example 22D vectors VctA = (3, 4), VctB = (1, 0)
Vector ▸ 2D vectors → enter A, B → FUNCTION
2D Result
VctA · VctB3
VctA × VctB−4
|VctA|5
Angle53.1301023542
In 2D the cross product is a single scalar (−4). |VctA| = √(3² + 4²) = 5, and the angle between the vectors is 53.13°.
Example 3The unit vector  of VctA = (3, 4)
FUNCTION ▸ Unit Vector Â
Unit Vector
|VctA|5
 (unit)(0.6, 0.8)
The unit vector  = A / |A| = (3/5, 4/5) = (0.6, 0.8) has length 1 and points the same way as A.
NoteThe angle uses the current Angle Unit. In Radian mode the same vectors give the angle in radians instead of degrees.
Ratio App Reference
RatioSolving proportions
The Ratio app finds the missing term X in a proportion A : B = C : D. Choose which position is unknown, enter the three known values, and the calculator solves for X by cross-multiplication.
Choosing the form
Ratio Form
1A : B = X : D
2A : B = C : X
Form 1 solves for the third term; form 2 solves for the fourth. Both use the rule that equal ratios cross-multiply: A · D = B · C.
Example 1To solve 3 : 4 = X : 8
Ratio ▸ A : B = X : D → 3, 4, 8 → FUNCTION
X = (A · D) / B = (3 · 8) / 4 = 6. This is just the proportion 3⁄4 = X⁄8, so 4X = 24.
Key operation:
3›EXE›4›EXE›8›EXE›FUNCTION
Example 2To solve 3 : 4 = 6 : X
Ratio ▸ A : B = C : X → 3, 4, 6 → FUNCTION
X = (B · C) / A = (4 · 6) / 3 = 8.
NoteTwo ratios are equal exactly when their cross-products match (A · D = B · C).
Spreadsheet App Reference
SpreadsheetA calculator spreadsheet
The Spreadsheet app is a grid of 5 columns (A–E) × 45 rows. Each cell holds either a number or a formula that begins with = and may reference other cells (A1, B2, …). Formulas recalculate automatically as you edit.
Entering constants
Move the cursor with the arrow keys and type a number to enter a constant into a cell. Press EXE to confirm and drop to the next row. The examples in this chapter build on column A holding the values 1 to 5.
Example 1To enter the values 1–5 into cells A1 to A5
Spreadsheet → point to A1 → 1 EXE 2 EXE …
Each value is typed and confirmed with EXE, which moves down to the next cell. The reference of a cell is its column letter and row number, so the value 3 sits in A3.
Entering formulas
Start a cell with = to make it a formula. A formula may contain numbers, operators and cell references (A1, B2, …). A reference always tracks the current value of that cell, so the formula recalculates automatically whenever the referenced cell changes.
Example 2To put =A1×2 in cell B1
point to B1 → = A1 × 2 EXE
B1 shows its computed value 2 (= 1 × 2). If you later change A1, B1 updates by itself. Use Show Cell (TOOLS) to view the underlying formula =A1×2 instead of the value.
Relative and absolute references
When a formula is copied or filled to another cell, its references shift with it — these are relative references. A $ locks part of a reference so it does not shift: $A$1 is fully locked, A$1 locks only the row and $A1 only the column.
Example 3To fill =A1×2 down column B (relative reference)
B1 → TOOLS ▸ Fill Formula → range B1:B5 → EXE
Filling adjusts the relative reference for each row: B2 becomes =A2×2, B3 becomes =A3×2, and so on — giving 2, 4, 6, 8, 10.
Example 4To fill =A1×$A$5 down column C (absolute reference)
C1 → TOOLS ▸ Fill Formula → range C1:C5 → EXE
The $A$5 part is locked to cell A5 (= 5) in every row, while A1 shifts to A2, A3, … So the column becomes A × 5 = 5, 10, 15, 20, 25.
Range commands — Sum, Min, Max, Mean
The commands Sum(, Min(, Max( and Mean( operate over a block of cells written as a range such as A1:A5. Insert them from the SHEET commands in the CATALOG.
Example 5To total column A with =Sum(A1:A5)
CATALOG ▸ SHEET ▸ Sum( → A1:A5 → EXE
Sum adds every value in the range: 1 + 2 + 3 + 4 + 5 = 15.
Example 6To find the mean, maximum and minimum of A1:A5
CATALOG ▸ SHEET ▸ Mean( / Max( / Min( → A1:A5 → EXE
Range commands
=Mean(A1:A5)3
=Max(A1:A5)5
=Min(A1:A5)1
Mean returns the average (15 ÷ 5 = 3), while Max and Min return the largest and smallest values in the range.
The spreadsheet TOOLS menu
Press TOOLS inside the sheet for editing commands that act on the pointed cell or range:
| Command | What it does |
| Fill Formula | Copies a formula across a range, adjusting relative references (locked $ parts stay put). |
| Fill Value | Writes the same constant into every cell of a range. |
| Copy & Paste | Duplicates a cell, adjusting its relative references at the destination. |
| Cut & Paste | Moves a cell; references are kept and the source is cleared. |
| Grab | Point to a cell to insert its reference into the formula you are editing. |
| Show Cell | Toggles the grid between showing computed values and the underlying formulas. |
| Auto Calc | Turns automatic recalculation on or off; Recalculate refreshes on demand. |
| Delete All | Clears the whole spreadsheet. |
Important!The spreadsheet holds up to 5 × 45 = 225 cells. Turning Auto Calc off freezes the displayed values — useful while entering a large sheet — until you Recalculate.
Math Box App Reference
Math BoxLearning-support tools
The Math Box app is a set of interactive learning aids: probability experiments and visual number tools. Choose a tool from the menu.
The Math Box menu
Math Box
1Dice Roll
2Coin Toss
3Number Line
4Circle
Each tool runs an experiment or draws a figure you can explore. Point to a tool and press OK.
Example 1Dice Roll — 2 dice, 20 rolls
Math Box ▸ Dice Roll → dice 2, attempts 20 → EXE
Rolls 1–3 dice for a chosen number of attempts and tallies each outcome — a hands-on way to see experimental probability approach the theoretical values. The Same Result setting (Off / #1 / #2 / #3) replays a fixed random sequence so a whole class sees identical rolls.
Example 2Coin Toss — 2 coins, 20 tosses
Math Box ▸ Coin Toss → coins 2, attempts 20 → EXE
With two coins the middle outcome (one head, one tail) is about twice as likely as two heads or two tails — visible directly in the tally.
Example 3Number Line — draw 2 ≤ x < 5
Math Box ▸ Number Line ▸ a ≤ x < b → 2, 5
Number Line
2 ≤ x < 5
●━━━━○ [2, 5)
Draws the solution of a simple inequality: a filled circle for an inclusive bound, an open circle for a strict one. Nine expression types are available, from x < a to a ≤ x ≤ b.
Example 4Circle — the Unit Circle at 30°
Math Box ▸ Circle ▸ Unit Circle
Unit Circle
Angle30°
cos θ (x)0.8660254038
sin θ (y)0.5
Displays a Unit Circle, Half Circle or Clock. At 30° the point is (cos 30°, sin 30°) = (√3⁄2, 1⁄2) ≈ (0.866, 0.5) — a visual link between angles and coordinates.
NoteMath Box tools are for exploration and teaching; they don't feed results into the other apps, but the frequency tables and coordinates can be read off directly.
Constants & Unit Conversions
Physical ConstantsCATALOG → CONST ▸
The CONST ▸ sub-menu inserts any of these 47 scientific constants (CODATA-based values) into a calculation. Point to a category, then to a constant, and press OK to insert its symbol and value. The six categories and their constants are:
Universal
| Symbol | Constant | Value | Unit |
|---|
| h | Planck constant | 6.62607015 × 10⁻³⁴ | J·s |
| ħ | reduced Planck constant (h/2π) | 1.054571817 × 10⁻³⁴ | J·s |
| c | speed of light in vacuum | 2.99792458 × 10⁸ | m/s |
| ε₀ | electric constant | 8.8541878188 × 10⁻¹² | F/m |
| μ₀ | magnetic constant | 1.25663706127 × 10⁻⁶ | N/A² |
| Z₀ | vacuum impedance | 376.730313412 | Ω |
| G | gravitational constant | 6.6743 × 10⁻¹¹ | m³·kg⁻¹·s⁻² |
| lP | Planck length | 1.616255 × 10⁻³⁵ | m |
| tP | Planck time | 5.391247 × 10⁻⁴⁴ | s |
Electromagnetic
| Symbol | Constant | Value | Unit |
|---|
| μN | nuclear magneton | 5.0507837393 × 10⁻²⁷ | J/T |
| μB | Bohr magneton | 9.2740100657 × 10⁻²⁴ | J/T |
| e | elementary charge | 1.602176634 × 10⁻¹⁹ | C |
| Φ₀ | magnetic flux quantum | 2.067833848 × 10⁻¹⁵ | Wb |
| G₀ | conductance quantum | 7.748091729 × 10⁻⁵ | S |
| KJ | Josephson constant | 4.835978484 × 10¹⁴ | Hz/V |
| RK | von Klitzing constant | 25812.80745 | Ω |
Atomic & Nuclear
| Symbol | Constant | Value | Unit |
|---|
| mp | proton mass | 1.67262192595 × 10⁻²⁷ | kg |
| mn | neutron mass | 1.67492750056 × 10⁻²⁷ | kg |
| me | electron mass | 9.1093837139 × 10⁻³¹ | kg |
| mμ | muon mass | 1.883531627 × 10⁻²⁸ | kg |
| a₀ | Bohr radius | 5.29177210544 × 10⁻¹¹ | m |
| α | fine-structure constant | 0.0072973525643 | — |
| re | classical electron radius | 2.8179403205 × 10⁻¹⁵ | m |
| λC | Compton wavelength | 2.42631023538 × 10⁻¹² | m |
| γp | proton gyromagnetic ratio | 2.6752218708 × 10⁸ | s⁻¹·T⁻¹ |
| λCp | proton Compton wavelength | 1.3214098536 × 10⁻¹⁵ | m |
| λCn | neutron Compton wavelength | 1.31959090382 × 10⁻¹⁵ | m |
| R∞ | Rydberg constant | 1.09737315682 × 10⁷ | m⁻¹ |
| μp | proton magnetic moment | 1.41060679545 × 10⁻²⁶ | J/T |
| μe | electron magnetic moment | −9.2847646917 × 10⁻²⁴ | J/T |
| μn | neutron magnetic moment | −9.6623653 × 10⁻²⁷ | J/T |
| μμ | muon magnetic moment | −4.4904483 × 10⁻²⁶ | J/T |
| mτ | tau mass | 3.16754 × 10⁻²⁷ | kg |
Physico-Chem
| Symbol | Constant | Value | Unit |
|---|
| mu | atomic mass constant | 1.66053906892 × 10⁻²⁷ | kg |
| F | Faraday constant | 96485.33212 | C/mol |
| NA | Avogadro constant | 6.02214076 × 10²³ | mol⁻¹ |
| k | Boltzmann constant | 1.380649 × 10⁻²³ | J/K |
| Vm | molar volume of ideal gas | 0.02271095464 | m³/mol |
| R | molar gas constant | 8.314462618 | J·mol⁻¹·K⁻¹ |
| c₁ | first radiation constant | 3.741771852 × 10⁻¹⁶ | W·m² |
| c₂ | second radiation constant | 0.01438776877 | m·K |
| σ | Stefan-Boltzmann constant | 5.670374419 × 10⁻⁸ | W·m⁻²·K⁻⁴ |
Adopted Values
| Symbol | Constant | Value | Unit |
|---|
| gn | std acceleration of gravity | 9.80665 | m/s² |
| atm | standard atmosphere | 101325 | Pa |
| RK-90 | conventional von Klitzing | 25812.807 | Ω |
| KJ-90 | conventional Josephson | 4.835979 × 10¹⁴ | Hz/V |
Other
| Symbol | Constant | Value | Unit |
|---|
| t | Celsius temperature (0 °C) | 273.15 | K |
NoteValues follow the 2022 CODATA recommended set. A constant is inserted as its stored value; combine it with other terms just like any number.
Unit ConversionsCATALOG → CONV ▸
The CONV ▸ sub-menu converts the value currently on the display. First compute or type a value, then choose a category and a conversion; the display is replaced by the converted value. There are 40 conversions in nine categories:
Length
| Conversion | Factor |
|---|
| in ▶ cm | × 2.54 |
| cm ▶ in | ÷ 2.54 |
| ft ▶ m | × 0.3048 |
| m ▶ ft | ÷ 0.3048 |
| yd ▶ m | × 0.9144 |
| m ▶ yd | ÷ 0.9144 |
| mile ▶ km | × 1.609344 |
| km ▶ mile | ÷ 1.609344 |
| n mile ▶ m | × 1852 |
| m ▶ n mile | ÷ 1852 |
| pc ▶ km | × 3.0856776 × 10¹³ |
| km ▶ pc | ÷ 3.0856776 × 10¹³ |
Area
| Conversion | Factor |
|---|
| acre ▶ m² | × 4046.856422 |
| m² ▶ acre | ÷ 4046.856422 |
Volume
| Conversion | Factor |
|---|
| gal(US) ▶ L | × 3.785411784 |
| L ▶ gal(US) | ÷ 3.785411784 |
| gal(UK) ▶ L | × 4.54609 |
| L ▶ gal(UK) | ÷ 4.54609 |
Mass
| Conversion | Factor |
|---|
| oz ▶ g | × 28.349523125 |
| g ▶ oz | ÷ 28.349523125 |
| lb ▶ kg | × 0.45359237 |
| kg ▶ lb | ÷ 0.45359237 |
Velocity
| Conversion | Factor |
|---|
| km/h ▶ m/s | ÷ 3.6 |
| m/s ▶ km/h | × 3.6 |
Pressure
| Conversion | Factor |
|---|
| atm ▶ Pa | × 101325 |
| Pa ▶ atm | ÷ 101325 |
| mmHg ▶ Pa | × 133.322387415 |
| Pa ▶ mmHg | ÷ 133.322387415 |
| kgf/cm² ▶ Pa | × 98066.5 |
| Pa ▶ kgf/cm² | ÷ 98066.5 |
| lbf/in² ▶ kPa | × 6.894757293 |
| kPa ▶ lbf/in² | ÷ 6.894757293 |
Energy
| Conversion | Factor |
|---|
| kgf·m ▶ J | × 9.80665 |
| J ▶ kgf·m | ÷ 9.80665 |
| J ▶ cal₁₅ | ÷ 4.1858 |
| cal₁₅ ▶ J | × 4.1858 |
Power
| Conversion | Factor |
|---|
| hp ▶ kW | × 0.745699872 |
| kW ▶ hp | ÷ 0.745699872 |
Temperature
| Conversion | Factor |
|---|
| °F ▶ °C | (x − 32) × 5⁄9 |
| °C ▶ °F | x × 9⁄5 + 32 |
NoteFactors follow NIST Special Publication 811. Each conversion has a matching reverse conversion (for example in ▶ cm and cm ▶ in), so you can convert in either direction.
Technical Reference
Calculation Priority SequenceOrder of operations
The calculator evaluates an expression according to a fixed priority sequence. Basically, calculations run from left to right, expressions inside parentheses have the highest priority, and each command has the priority shown below.
| Priority | Commands |
| 1 | Parenthetical expressions |
| 2 | Functions that take parentheses — sin(, cos(, tan(, ln(, log(, √, ∛, log▢(, Abs(, GCD(, LCM(, d/dx, ∫dx, Σ, Π, Pol(, Rec( and similar |
| 3 | Functions that come after a value — x², x³, x⁻¹, x!, %, angle units ° ʳ ᵍ — and powers (x▢) and roots (▢√▢) |
| 4 | Negative sign (−) and Base-N prefixes (d, h, b, o) |
| 5 | Permutation (nPr), combination (nCr), complex polar symbol (∠) |
| 6 | Implicit multiplication — an omitted × before a value, constant or bracket (2π, 3(1+2)) |
| 7 | Multiplication (×), division (÷), dot product (·) |
| 8 | Addition (+), subtraction (−) |
| 9 | and (logical operator, Base-N) |
| 10 | or, xor, xnor (logical operators, Base-N) |
Important!Implicit multiplication (priority 6) binds tighter than explicit × and ÷ (priority 7). This is why 6 ÷ 2(1 + 2) = 1 — the calculator reads it as 6 ÷ (2 × (1 + 2)) — and 6 ÷ 2π = 0.9549… reads as 6 ÷ (2π).
Precautions when a calculation contains negative values
Because a postfix function such as x² (priority 3) binds tighter than the negative sign (priority 4), a leading minus applies to the whole power. To square a negative value you must enclose it in parentheses.
−2²=−4
reads −(2²): the square is taken first, then negated
(−2)²=4
the parentheses square the whole value −2
Calculation Ranges, Digits and PrecisionHow the emulator computes
The SC-991BF emulator performs every calculation in IEEE-754 double precision — the same arithmetic used throughout modern computing — and then formats the answer the way a scientific calculator would.
| Property | Value |
| Internal precision | Double precision — about 15–16 significant digits |
| Displayed digits (Norm) | Up to 10 significant digits |
| Switch to scientific form | When |x| ≥ 1×10¹⁰ or |x| < 1×10⁻⁹ (Norm 2, default); < 1×10⁻² in Norm 1 |
| Fix setting | Fixed number of decimal places, 0 to 9 |
| Sci setting | Fixed number of significant figures |
NoteErrors are cumulative across consecutive calculations, and tend to be larger near a function's singular points and inflection points. Functions that need repeated internal calculation — xʸ, ˣ√y, x!, nPr, nCr, numerical d/dx and ∫dx — can accumulate error with each step.
Function input ranges
The following table lists the practical input range of the main functions. Values outside a range give a Math ERROR.
| Function | Input range |
| sin x, cos x, tan x | Degree: |x| < 9×10⁹ · Radian: |x| < 157079632.7 · (tan x undefined at odd multiples of 90°) |
| sin⁻¹x, cos⁻¹x | 0 ≤ |x| ≤ 1 |
| tan⁻¹x | |x| ≤ 9.999999999×10⁹⁹ |
| sinh x, cosh x | |x| ≤ 230.2585092 |
| sinh⁻¹x | |x| ≤ 4.999999999×10⁹⁹ |
| cosh⁻¹x | 1 ≤ x ≤ 4.999999999×10⁹⁹ |
| tanh x | |x| ≤ 9.999999999×10⁹⁹ |
| tanh⁻¹x | |x| ≤ 9.999999999×10⁻¹ |
| log x, ln x | 0 < x ≤ 9.999999999×10⁹⁹ |
| 10ˣ | −9.999999999×10⁹⁹ ≤ x ≤ 99.99999999 |
| eˣ | −9.999999999×10⁹⁹ ≤ x ≤ 230.2585092 |
| √x | 0 ≤ x < 1×10¹⁰⁰ |
| x² | |x| < 1×10⁵⁰ |
| x⁻¹ | |x| < 1×10¹⁰⁰; x ≠ 0 |
| x! | 0 ≤ x ≤ 69 (x is an integer) |
| nPr, nCr | 0 ≤ r ≤ n; n < 1×10¹⁰ (n, r integers) |
| Pol(x, y) | |x|, |y| ≤ 9.999999999×10⁹⁹ |
| Rec(r, θ) | 0 ≤ r ≤ 9.999999999×10⁹⁹; θ same as sin x |
| RanInt#(a, b) | a < b; |a|, |b| < 1×10¹⁰ |
| GCD(a, b), LCM(a, b) | integers, |a|, |b| < 1×10¹⁰ |
NoteThe Base-N app works only with integers in the signed 32-bit range −2 147 483 648 to 2 147 483 647; a result outside this range is a Math ERROR.
Error MessagesCauses and remedies
When a calculation cannot be completed, the calculator shows an error message instead of a result. Press ◀ or ▶ to return to the expression with the cursor at the position of the problem, correct it, and try again. The common messages are:
| Message | Cause | Remedy |
| Syntax ERROR | The expression is not written correctly — for example mismatched parentheses, or an operator with a missing operand. | Check the input at the cursor and correct the format. |
| Math ERROR | The calculation is mathematically undefined or out of range — division by zero, √ of a negative in real mode, or a value outside a function's input range (see the table above). | Check the values. For a square root or power that gives a complex result, use the Complex app. |
| Dimension ERROR | A matrix or vector operation was attempted on incompatible sizes — for example adding matrices of different dimensions, or multiplying when the columns of the first do not equal the rows of the second. | Re-enter the matrices or vectors with compatible dimensions. |
| Square only | A determinant or inverse was requested for a matrix that is not square. | Use a square matrix (equal rows and columns). |
| Cannot Solve | SOLVE could not find a root of the equation starting from the current value of x. | Store a different starting value in x, closer to the expected root, and solve again. |
NoteSome apps also show short guidance messages such as No data, No equation, f(x) empty or Empty. These are not errors — they simply mean the app needs you to enter its data or expression before it can calculate.
SpecificationsEmulator & platforms
| Product | eBidyaloy SC-991BF — scientific calculator emulator |
| Platforms | Windows, macOS, Web, Android and iOS |
| Calculator apps | 13 (Calculate, Statistics, Distribution, Table, Equation, Inequality, Complex, Matrix, Vector, Spreadsheet, Ratio, Math Box, Base-N) |
| Display | Natural textbook display (MathI/MathO) with an optional enlarged “extended display” for classrooms |
| Variable memories | A, B, C, D, E, F, x, y, z, M, plus Ans and MatAns |
| Matrix memories | MatA, MatB, MatC, MatD (up to 4×4) |
| Physical constants | 47 constants in 6 categories (CODATA-based) |
| Unit conversions | 40 conversions in 9 categories |
| Internal precision | IEEE-754 double precision (~15 significant digits) |
| Power | None required — the emulator is software and is always ready to use on the host device |
NoteBecause the SC-991BF is a software emulator, there is no battery to replace and no low-battery warning: it is available whenever the app or web page is open, and its speed depends on the host device.
Frequently Asked Questions
Frequently Asked Questions
How can I change a fraction result to decimal form?
While a fraction result is on screen, press ⇄ (FORMAT / S⇔D) to toggle between the exact form (fraction, π, √) and a decimal. To make results appear as decimals from the start, change Input/Output in SETTINGS to MathI/DecimalO.
What is the difference between Ans memory and variable memory?
Both store a single value. Ans holds the result of the last calculation, letting you carry it straight into the next one (press Ans). A variable (A–F, x, y, z, M) is a named container you fill yourself and reuse whenever you need the same value more than once.
How can I find a function from an older calculator model?
Almost every function lives on the CATALOG. Press CATALOG to open the catalog menu, then pick the function or constant you need. See Using the CATALOG earlier in this guide for the full list.
How do I change the calculation result display format?
Press ⇄ (FORMAT) after a result to cycle exact ⇄ decimal, or open the TOOLS menu for Prime Factor, Recurring Decimal, Sexagesimal and Improper/Mixed Fraction. Result defaults are set in SETTINGS (Number Format, Fraction Result, Complex Result).
How can I tell which calculator app I am currently using?
Press ⌂ (HOME). The icon of the app you are in is highlighted on the HOME screen.
How do I calculate sin² x ?
sin²x means (sin x)². Enter it as the square of the sine — for example sin²30° = (sin 30°)² = ¼:
(›sin›3›0›)›▢²›EXE
Why can’t I input i or calculate with complex numbers in Calculate?
The Calculate app works with real numbers. To enter the imaginary unit i or perform complex arithmetic, switch to the Complex app.
How can I return the calculator to its initial default settings?
Open any app from HOME, then press ⚙ (SETTINGS) and choose Reset ▸ Settings & Data ▸ Yes. This restores the default settings and clears memories.
Do I need to worry about the battery?
No. The SC-991BF is a software emulator, so it has no battery, never shows a low-battery warning, and is ready whenever you open it.