Natural family

Natural Scientific 991 quick reference

A textbook-style scientific calculator: fractions, roots, powers and integrals are typed and shown in natural form, and exact answers such as fractions and square roots are kept when possible. The MENU key opens apps such as statistics, matrices, equations and tables.

Main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on. · Shift layer: SHIFT · Second layer: ALPHA

Open in Trident

Keys

Menus and screens

MENU: Calculate (1)

The normal calculation screen with natural input and output.

MENU: Complex (2)

Calculations with i, plus argument, conjugate and polar conversions in OPTN.

MENU: Base-N (3)

Binary, octal, decimal and hexadecimal arithmetic with logic operators in OPTN.

MENU: Matrix and Vector (4, 5)

Define matrices A to D or vectors, then calculate with them. OPTN lists the operations.

MENU: Statistics (6)

Pick a regression type, enter data in the editor, then read the results.

MENU: Distribution (7)

Normal, binomial and Poisson probabilities.

MENU: Table (9)

Builds a table of values for a function over a range.

MENU: Equation/Func (A)

Solves 2 to 4 simultaneous equations or polynomials of degree 2 to 4.

MENU: Ratio (C)

Solves proportion problems. Spreadsheet (8) and Inequality (B) are not available yet.

OPTN

Context menu: hyperbolic functions, angle units, Pol/Rec, rounding, GCD, LCM, or app-specific tools.

Modes and settings

Input/Output

SHIFT then MENU (SETUP): natural math or plain line display, with exact or decimal answers.

Angle unit

Degree, radian or gradian for trig functions, in SETUP.

Number format

Fix (set decimals), Sci (significant digits) or Norm 1 and 2, in SETUP.

Fraction result

Mixed fractions or improper fractions, in SETUP.

Complex format

Rectangular (a+bi) or polar (r∠θ), in SETUP.

Statistics frequency

Turns the frequency column in the statistics editor on or off.

Reset

SHIFT then 9: reset setup data, variable memory, or everything.

Tips

• Press S⇔D to switch an answer between exact form (fraction or root) and decimal.
• SHIFT then = (≈) forces a decimal answer for the current line.
• Use the arrow keys to move through the template boxes in fractions and powers.
• Press the up arrow on an empty line to bring back a previous calculation and edit it.
• Store a value with SHIFT RCL (STO) then a variable key; recall it by typing the letter with ALPHA.
• CALC asks for the value of each variable in an expression, so you can re-run it with new numbers.

Guides for this calculator

• Do basic arithmeticAdd, subtract, multiply and divide, and see how each calculator family shows the answer.
• Enter and calculate with negative numbersUse the negative-sign key (not the subtract key) so a number really becomes negative.
• Work with fractionsAdd, subtract, multiply and divide fractions and get an exact fraction back.
• Convert between fractions and decimalsTurn 0.75 into 3/4, or 3/8 into 0.375.
• Powers and exponentsSquare a number or raise it to any power such as 2 to the 10th.
• Find a square rootGet the square root of a number, exactly or as a decimal.
• Cube roots and other rootsFind any root of a number, such as the cube root of 27.
• Find a percentage of a numberWork out 15% of 200 with the percent key or by dividing by 100.
• Reuse the last answerCarry the previous result into your next calculation without retyping it.
• Evaluate an expression for a value of xFind the value of 3x² − 2x + 1 when x is 4.
• Solve a linear equationFind x in an equation like 3x + 5 = 20.
• Solve a quadratic equationFind the roots of x² − 5x + 6 = 0 with a polynomial solver or the quadratic formula.
• Solve a system of two equationsFind x and y when 2x + y = 5 and x − y = 1.
• Solve a system of three equationsFind x, y and z for three linked equations.
• Absolute valueFind how far a number is from zero, ignoring its sign.
• Round answers to a set number of decimalsChange the display so every answer shows, say, 2 decimal places.
• Greatest common divisor and least common multipleFind the largest number that divides two numbers (GCD) and the smallest number both divide (LCM).
• Use the Pythagorean theoremFind the long side (hypotenuse) of a right triangle from the two shorter sides.
• Distance between two pointsFind how far apart two points are on a graph, using the distance formula.
• Find the midpoint of a segmentAverage the x values and the y values of two points to find the point halfway between them.
• Find the slope of a lineWork out rise over run between two points, such as (2, 1) and (6, 4).
• Area of a circleUse A = πr² to find the area of a circle with radius 5.
• Area of a triangleFind a triangle area from base and height, or from three side lengths with Heron's formula.
• Volume of a cylinderUse V = πr²h for a cylinder with radius 3 and height 10.
• Volume of a sphereUse V = (4/3)πr³ for a sphere with radius 6.
• Volume of a coneUse V = (1/3)πr²h for a cone with radius 3 and height 7.
• Surface area of a boxAdd the area of all six faces of a rectangular box (8 by 5 by 3).
• Angles in a polygonFind the sum of the inside angles and the size of each angle in a regular polygon.
• Degrees, minutes and secondsConvert an angle between decimal degrees (35.5125) and degrees-minutes-seconds (35°30'45").
• Set degrees or radiansTell the calculator whether angles are measured in degrees or radians before you use sin, cos or tan.
• Find sine, cosine and tangentGet sin, cos or tan of an angle, here sin 50, cos 50 and tan 50 in degrees.
• Find an angle from a ratioUse the inverse trig functions (sin⁻¹, cos⁻¹, tan⁻¹) to turn a ratio back into an angle.
• Convert between degrees and radiansChange an angle from degrees to radians and back with the calculator.
• Solve a right triangleFind a missing side from the hypotenuse and an angle, and a missing angle from two sides.
• Use the law of sinesFind a side of any triangle when you know the opposite angle of another side and its length.
• Use the law of cosinesFind the third side of a triangle when you know two sides and the angle between them.
• Secant, cosecant and cotangentGet sec, csc and cot by taking the reciprocal of cos, sin and tan.
• Convert between polar and rectangularTurn a point (x, y) into a distance r and an angle θ.
• Check unit circle valuesFind the exact values of sin, cos and tan at 30, 45 and 60 degrees.
• Hyperbolic functionsFind sinh, cosh and tanh with the hyperbolic menu.
• Make a table of valuesList x and f(x) side by side for a function, starting wherever you like.
• Work with logarithmsFind log base 10 of a number and undo it with 10 to a power.
• Natural logs and the number eUse ln and eˣ, the natural log and its inverse, based on e ≈ 2.71828.
• Logarithm with any baseFind a log such as log base 2 of 20 by dividing two natural logs.
• Exponential growthFind what a quantity grows to at a fixed percentage rate, and how long it takes to double.
• Complex numbersMultiply complex numbers like (3 + 4i)(1 − 2i) and find a size (modulus) such as |3 + 4i|.
• Enter and multiply matricesStore the matrix [[1, 2], [3, 4]] and multiply it by itself.
• Matrix determinant and inverseFind the determinant and inverse of [[1, 2], [3, 4]].
• Sum a sequence or seriesAdd up the first terms of a sequence, such as 1 + 3 + 5 + … + 19, which comes to 100.
• Find the slope of a function at a pointGet the derivative of a function at one x value as a decimal, using the built-in derivative function.
• Find a definite integralWork out the integral of a function between two x values and get a number.
• Solve an equation numericallyFind a root of any equation by giving a starting guess and letting the calculator home in on the answer.
• Add up a series (sigma notation)Find the sum of an expression as the counter runs from a start to an end value.
• Enter data into a listType a set of numbers into a list so you can summarise, plot or fit them.
• Find the mean and spread of one listGet the count, sum, mean and standard deviation of a list of numbers in one go.
• Fit a straight line to dataFind the least-squares line y = ax + b that best matches a set of points.
• Fit a parabola to dataFind the curve y = ax² + bx + c that best matches points that bend.
• Fit an exponential curve to dataFind y = a·b^x for data that grows or shrinks by a steady factor.
• Measure how strongly two lists are relatedFind the correlation coefficient r, which runs from -1 (perfect downhill) to +1 (perfect uphill).
• Find the mean, median and modeWork out the average (mean), the middle value (median) and the most common value (mode) of a list.
• Find the standard deviationMeasure how spread out a list is, using the sample or the population formula.
• Use frequencies (how many times each value occurs)Enter each value once with a count beside it instead of typing it over and over.
• Find a probability on a normal curveWork out the chance that a normally distributed value lands between two numbers.
• Find the value for a given percentileGo backwards from an area on the normal curve to the number that cuts it off.
• Binomial probabilitiesFind the chance of getting exactly a certain number of successes in a fixed number of tries.
• Poisson probabilitiesFind the chance of a certain number of events in a fixed time or space, given their average rate.
• Generate random numbersGet a random decimal between 0 and 1, or a random whole number in a range such as a dice roll.
• Count arrangements and selections (nPr and nCr)Count how many ways to arrange or choose items from a group.
• Calculate a factorialMultiply a whole number by every whole number below it, such as 6! = 720.
• Find a weighted meanAverage values when some count for more than others, such as graded work with different weights.
• Simple interestInterest on a fixed amount that does not itself earn interest: I = P × r × t.
• Compound interestGrowth where interest is added to the balance and then earns interest itself.
• Percent change between two numbersFind how much a value rose or fell, as a percentage of where it started.
• Break-even pointHow many units must you sell before income covers your costs?
• Enter very big and very small numbersType numbers like 6.022 × 10²³ with the exponent key and read answers shown in scientific notation.
• Show answers in engineering notationDisplay results with powers of ten that are multiples of three, like 47 × 10³ for 47 kilo-units.
• Round an answer to significant figuresShow a result with the right number of significant figures, and see how to count them.
• Use a physical constant in a formulaEnter constants such as the speed of light correctly, store them for reuse, and see them in the Units lab.
• Convert between unitsChange miles per hour to metres per second (or any unit) by multiplying by conversion factors.
• Calculate molar massAdd up the atomic masses of every atom in a formula, like glucose C₆H₁₂O₆, to get grams per mole.
• Use the ideal gas lawFind the volume of a gas from PV = nRT, with moles, temperature and pressure.
• Solve a constant-acceleration motion problemUse s = ut + ½at² and v² = u² + 2as to find distance and final speed.
• Calculate pH and hydrogen-ion concentrationUse the log key for pH = -log[H⁺] and the 10ˣ key to go back from pH to concentration.
• Work out radioactive decay with half-lifeFind how much of a sample is left after some time, using N = N₀ × (1/2)^(t/T).
• Use Ohm's law and parallel resistorsFind the combined resistance of two resistors in parallel and then the current from V = IR.
• Calculate kinetic and potential energyFind kinetic energy with ½mv² and gravitational potential energy with mgh.