Fractions in the Display, Display Rules | HP 35s Scientific guide

If you didn't get the same results as the example, you may have accidentally changed how fractions are displayed. (See "Changing the Fraction Display" later in this chapter.)

The next topic includes more examples of valid and invalid input fractions.

Fractions in the Display

In Fraction–display mode, numbers are evaluated internally as decimal numbers, then they're displayed using the most precise fractions allowed. In addition, accuracy annunciators show the direction of any inaccuracy of the fraction compared to its 12–digit decimal value. (Most statistics registers are exceptions — they're always shown as decimal numbers.)

Display Rules

The fraction you see may differ from the one you enter. In its default condition, the calculator displays a fractional number according to the following rules. (To change the rules, see "Changing the Fraction Display" later in this chapter.)

The number has an integer part and, if necessary, a proper fraction (the numerator is less than the denominator).

The denominator is no greater than 4095.

The fraction is reduced as far as possible.

Examples:

These are examples of entered values and the displayed results. For comparison, the internal 12–digit values are also shown. The and annunciators in the last column are explained below.

5-2Fractions

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HP 35s Scientific manual Fractions in the Display, Display Rules, 2Fractions

Contents

HP 35s scientific calculator Users guide Printing History Contents RPN The Automatic Memory Stack Viewing a Variable ContentsStoring Data into Variables Trigonometry Entering π Real-Number FunctionsQuotient and Remainder of Division Hyperbolic Functions Fractions Entering and Evaluating Equations Operations with Complex Numbers Solving EquationsIntegrating Equations Vector Arithmetic 10-1 10-7 Base Conversions and Arithmetic and Logic 11-1Statistical Operations 12-1 Creating Vectors from Variables or Registers 10-8 Part 2. Programming Simple Programming 13-1 Programming Techniques 14-1 Solving and Integrating Programs 15-1 Support, Batteries, and ServicePart 3. Appendixes and Reference Statistics Programs 16-1 ALG Summary User Memory and the StackMore about Solving Messages Operation Index Round-Off ErrorMore about Integration How the Integral Is Evaluated Contents Part Page Important Preliminaries Adjusting Display ContrastGetting Started Turning the Calculator On and Off Shifted Keys Highlights of the Keyboard and Display2Getting Started Function Key Alpha KeysCursor Keys Left-shifted function Right-shifted Letter for alphabetic Keys for Clearing  Clear or CancelBackspacing and Clearing 4Getting Started Key Description Clear menu       HP 35s Menus Chapter Name Using Menusˆ ˆ    6Getting Started Programming Instructions Other functions  Exiting Menusor  8 Keys Display RPN and ALG Modes KeysDisplay RPN mode ALG mode 10Getting Started Undo key Annunciators Display and AnnunciatorsFirst Line Second Line 12Getting Started HP 35s Annunciators Meaning Chapter EQN 14Getting Started Making Numbers Negative Keying in NumbersExponents of Ten z 16Getting Started  Understanding Entry CursorRange of Numbers and Overflow  Single Argument or Unary Operations Performing Arithmetic Calculations18Getting Started  Two Argument or Binary OperationsKey RPN,RPN Program ALG, Equation, ALG Program   Õ Controlling the Display Format Key RPN, RPN Program ALG, Equation, ALG Program 22Getting Started Periods and Commas in Numbers   8 Complex number display format  ,  , 8 24Getting Started 8× SHOWing Full 12-Digit Precision8    Entering Fractions Fractions26Getting Started  É Messages  Checking Available Memory Calculator Memory28Getting Started Clearing All of Memory 30Getting Started What the Stack Is RPN The Automatic Memory StackRPN The Automatic Memory Stack 2RPN The Automatic Memory Stack Clearing the X-Register X and Y-Registers are in the DisplayReviewing the Stack Press  Exchanging the X- and Y-Registers in the Stack4RPN The Automatic Memory Stack Arithmetic How the Stack Does It How Enter Works 6RPN The Automatic Memory Stack How to Clear the Stack Filling the stack with a constant Last X Register 8RPN The Automatic Memory Stack Correcting Mistakes with Last  Reusing Numbers with Last Ù     Chain Calculations in RPN ModeWork from the Parentheses Out      ExercisesOrder of Calculation       More Exercises       18RPN The Automatic Memory Stack Keys DisplayDescription AStoring Data into Variables Press letter-key  Storing and Recalling Numbers2Storing Data into Variables Press letter-key  G  A  VAR catalog Using the MEM CatalogViewing a Variable 4Storing Data into Variables C D E 6Storing Data into Variables Arithmetic with Stored VariablesStorage Arithmetic Storage arithmetic uses , , , or  Recall Arithmetic D Exchanging x with Any Variable D E  Variables I and JA 10Storing Data into Variables Exponential and Logarithmic Functions Real-Number Functions   Power FunctionsQuotient and Remainder of Division   Trigonometry Entering π Option Description Annunciator Setting the Angular ModeTrigonometric Functions 4Real-Number Functions   Hyperbolic Functions Percentage Functions     Const Menu Items Description Value Physics Constants8Real-Number Functions Items Description Value Rectangular/Polar Conversions Conversion Functions10Real-Number Functions 30o 6 812Real-Number Functions Angle Conversions Time Conversions Unit Conversions Gamma Probability FunctionsFactorial Probability  16Real-Number Functions Fractional part Parts of NumbersInteger part Absolute value PressDisplay To calculate18Real-Number Functions Entering Fractions Fractions  Display Rules Fractions in the Display2Fractions Accuracy Indicators Entered Value Internal Value Displayed Fraction Changing the Fraction Display Setting the Maximum Denominator4Fractions  Choosing a Fraction Format 6Fractions   j To Get This Fraction Format Change These Flags Rounding Fractions Examples of Fraction Displays Fractions in Equations Fractions in Programs 10Fractions Entering and Evaluating Equations Entering and Evaluating EquationsHow You Can Use Equations = .25 π d2 l 2Entering and Evaluating Equations    D Value   Summary of Equation Operations Key Operation Variables in Equations Entering Equations into the Equation List4Entering and Evaluating Equations Numbers in Equations Functions in Equations   Displaying and Selecting EquationsParentheses in Equations  Ö  Editing and Clearing Equations 8Entering and Evaluating Equations Types of Equations Evaluating Equations 10Entering and Evaluating Equations Using Enter for Evaluation Type of Equation Result for  Result for        Using XEQ for Evaluation12Entering and Evaluating Equations  Responding to Equation Prompts Operator Precedence Syntax of Equations14Entering and Evaluating Equations Order Operation Example Equations Meaning 16Entering and Evaluating Equations Equation FunctionsΣxy RPN Operation Equation function Perimeter = a + b + h sin1θ + sin1φ 18Entering and Evaluating Equations Area = Verifying Equations Syntax Errors Õ 20Entering and Evaluating Equations Solving Equations Solving EquationsSolving an Equation Markup ⋅ Cost = Price 2Solving Equations = v0 t + 1/2 g t G    P       P    Solving built-in Equation 6Solving Equations Verifying the Result Understanding and Controlling Solve Choosing Initial Guesses for Solve Interrupting a Solve Calculation8Solving Equations Solving Equations Type in the equation 10Solving Equations= 40 H ⋅ 20 H ⋅ 4 ⋅ H Equation H   4H  value For More Information 12Solving Equations Integrating Equations Integrating Equations Integrating Equations FN 2Integrating Equations J0 x = π 0 cosx sin t dt   = t 4Integrating Equations X  SinxX Interpreting Accuracy Accuracy of IntegrationSpecifying Accuracy 6Integrating Equations 8        8 8Integrating Equations Operations with Complex Numbers Form  Complex Operations Complex Stack2Operations with Complex Numbers Functions for One Complex Number, z To Calculate Press Display Description 8  68  6 6 6 4Operations with Complex Numbers Using Complex Numbers in Polar Notation ?  ?  ?  6Operations with Complex Numbers Complex Numbers in Equations 6 ? ?    Program lines ALG modeComplex Number in Program        Vector operations Vector ArithmeticVector Arithmetic  Õ 3    Absolute value of the vector  3  3 3 Dot product   10-4Vector Arithmetic   Angle between vectors Õ 3   3   Vectors in Equations10-6Vector Arithmetic Vectors in Programs Program lines Description Then hC Õ hA Creating Vectors from Variables or Registers10-8Vector Arithmetic Menu label Description Base Conversions and Arithmetic and LogicBase Menu Base Conversions and Arithmetic and Logic    11-2Base Conversions and Arithmetic and Logic Õ  Logic Menu Arithmetic in Bases 2, 8,11-4Base Conversions and Arithmetic and Logic            Representation of NumbersNegative Numbers  Range of Numbers  Using base in program and equationsWindows for Long Binary Numbers    Entering Statistical Data Statistical OperationsStatistical Operations Entering Two-Variable Data Correcting Errors in Data EntryEntering One-Variable Data 12-2Statistical Operations   Initial x, y Corrected x, y Statistics Menus Statistical CalculationsMean Menu Key Description      Sample Standard Deviation     Population Standard Deviation Linear Regression Linear Regression Menu  ˆ Õ ˆ12-8Statistical Operations         Limitations on Precision of Data12-10Statistical Operations Summation Values and the Statistics Registers Summation Statistics Access to the Statistics Registers 12-12Statistical Operations Statistical Operations 12-14Statistical Operations Programming Page Simple Programming Simple Programming 13-2Simple Programming Area = πx2 Designing a Program Selecting a ModeKeysDisplay In ALG mode  X  13-4Simple Programming Using RPN, ALG and Equations in ProgramsProgram Boundaries LBL and RTN  letter-key Data Input and Output Strengths of RPN Operations Entering a Program 13-6Simple Programming Clear functions and backspace key A Function Names in Programs13-8Simple Programming R RPN modeE  R   Running a ProgramExecuting a Program XEQ 13-10Simple Programming Keys Display Description RPN mode Testing a Program Entering and Displaying Data 13-12Simple Programming Using Input for Entering Data RPN mode ALG mode 13-14Simple Programming Using View for Displaying Data   ÇR ÇH Using Equations to Display Messages13-16Simple Programming  V OL  A RE A   Keys RPN mode R H V  R R H   V  S     13-18Simple Programming Displaying Information without Stopping  C  value Programming a Stop or Pause STOP, PSE Error StopsStopping or Interrupting a Program Interrupting a Running Program Editing a Program 13-20Simple Programming Program Memory Viewing Program Memory Catalog of Programs MEM Memory Usage13-22Simple Programming Clearing One or More Programs Checksum  Nonprogrammable FunctionsProgramming with Base   Decimal mode set Selecting a Base Mode in a ProgramNumbers Entered in Program Lines 13-26Simple Programming Polynomial Expressions and Horners MethodAx4 + Bx3 + Cx2 + Dx + E   A X     A  13-28Simple Programming Calling Subroutines XEQ, RTN Programming TechniquesRoutines in Programs Programming Techniques Nested Subroutines 14-2Programming Techniques A2 + b2 + c2 + d2 14-4Programming Techniques Branching GTOA2 + B2 Using GTO from the Keyboard Programmed GTO Instruction Conditional Instructions 14-6Programming Techniques Tests of Comparison x?y, x?0 Test Menus Program Lines Description RPN mode 14-8Programming Techniques Flags Meanings of Flags Clear Flag Fraction-Control Flags14-10Programming Techniques Programming Techniques Flags Menu 14-12Programming Techniques … takes the natural log of the X-input 14-14Programming Techniques  S  value   value Number F      Loops14-16Programming Techniques Conditional Loops GTO Loops with Counters DSE, ISG 14-18Programming Techniques Programming Techniques Variables I and J Indirectly Addressing Variables and Labels14-20Programming Techniques Indirect Address, I and J If I/J contains Then I/J will address 14-22Programming Techniques Equations with I/J Program Control with I/JUnnamed indirect variables 14-24Programming Techniques Solving a Program Solving and Integrating ProgramsSolving and Integrating Programs 15-2Solving and Integrating Programs V= N x R x T G Keys Display Description ALG modeProgram Lines Description ALG mode P  value   value H    P   L  15-6Solving and Integrating Programs Using Solve in a Program label  variable Program Lines In RPN mode Integrating a Program 15-8Solving and Integrating Programs  S   X Sin 15-10Solving and Integrating Programs Using Integration in a Program label   variable Restrictions on Solving and Integrating 15-12Solving and Integrating Programs Curve Fitting Statistics ProgramsStatistics Programs = B + MIn 16-2Statistics Programs Program Listing 16-4Statistics Programs    16-6Statistics Programs Determines if D001 or B001 should be run 16-8Statistics Programs S             Logarithmic Exponential PowerNormal and Inverse-Normal Distributions  Qx = 0.5 − σ 12π xx e−x −x ⎟σ 2 ⎟2dx 16-12Statistics Programs This routine initializes the normal distribution program Program Lines 16-14Statistics Programs Program Lines To the inverse S 16-16Statistics Programs Program D  16-18Statistics Programs Grouped Standard Deviation∑ x f   16-20Statistics Programs Statistics register Index variable used to indirectly address the correctRegister Summation Σ f Summation Σ x i f    U     16-24Statistics Programs Miscellaneous Programs and Equations Miscellaneous Programs and EquationsTime Value of Money TVM equation is I P4 NÕ I 17-4Miscellaneous Programs and Equations KeysDisplay In RPN mode    P  value     I 17-6Miscellaneous Programs and Equations Prime Number Generator   17-8Miscellaneous Programs and Equations Tests to see whether all possible factors have been tried   17-10Miscellaneous Programs and Equations Cross Product in Vectors 17-12Miscellaneous Programs and Equations z 17-14Miscellaneous Programs and Equations Appendixes and Reference Page Calculator Support Support, Batteries, and ServiceSupport, Batteries, and Service A-1 Answers to Common Questions 2Support, Batteries, and Service Environmental Limits Support, Batteries, and Service A-3 Changing the Batteries Testing Calculator Operation 4Support, Batteries, and Service Support, Batteries, and Service A-5 Self-Test 6Support, Batteries, and Service Warranty Support, Batteries, and Service A-7 8Support, Batteries, and Service Customer Support Support, Batteries, and Service A-9 Emea 10Support, Batteries, and Service Support, Batteries, and Service A-11 Invent 12Support, Batteries, and Service Support, Batteries, and Service A-13 Yyyy+ 14Support, Batteries, and Service Managing Calculator Memory User Memory and the StackUser Memory and the Stack B-1 Resetting the Calculator 2User Memory and the Stack Clearing Memory User Memory and the Stack B-3 Category DefaultStatus of Stack Lift 4User Memory and the Stack Neutral Operations Disabling OperationsUser Memory and the Stack B-5 ˆ ˆ Status of the Last X Register6User Memory and the Stack Accessing Stack Register Contents 8User Memory and the Stack , ALG SummaryAbout ALG ALG Summary C-1 Doing Two argument Arithmetic in ALG Simple Arithmetic Power Functions Percentage Calculations Quotient and Remainder Of Division Parentheses CalculationsPermutations and Combinations xÕ  4 Õ  Trigonometric Functions Hyperbolic functions Reviewing the Stack ALG Summary C-7 Operations with Complex Numbers Integrating an Equation8ALG Summary 6 ALG Summary C-9  8Ë4 66 6Õ4 6 Entering Statistical Two-Variable Data Z6 z Σ12ALG Summary   ˆ Õ ˆ ALG Summary C-13 14ALG Summary How Solve Finds a Root More about SolvingMore about Solving D-1 2More about Solving Function Whose Roots Can Be Found Interpreting Results More about Solving D-3 X X  X X  4More about Solving X  XX  XÕ  6More about Solving X Õ  X  X4 More about Solving D-7  X   When Solve Cannot Find a Root8More about Solving    XMore about Solving D-9  X  X   10More about Solving X4 X ÕÕ More about Solving D-11 X   12More about Solving  X   Round-Off ErrorMore about Solving D-13 14More about Solving How the Integral Is Evaluated More about IntegrationMore about Integration Conditions That Could Cause Incorrect Results 2More about Integration ∞ xe−xdx   4More about Integration More about Integration 6More about Integration Conditions That Prolong Calculation Time   8More about Integration More about Integration 10More about Integration Messages Messages F-1 2Messages Or program. This might take a while Messages F-3 4Messages    Solve include EQN and PGM modecannot find FN each uses a level, they can also generate this error Messages F-5 6Messages Name Keys and Description Operation IndexOperation Index G-1 Ø ×2Operation Index Operation Index G-3 = 4Operation Index Operation Index G-5  Denominator 6Operation Index label Operation Index G-7Natural exponential  Fractional part  8Operation Index Input variable variable Operation Index G-9  Integer part ISG variable variable LBL label label 10Operation Index Natural logarithm  Pause Operation Index G-11RCL variable Degrees to radians. Returns 2π/360 12Operation Index Operation Index G-13 View variable variable 14Operation IndexHyperbolic Tangent XEQ label label Õ≤ ÕÕ≠ Operation Index G-15 14-7 Menu ≠0? 16Operation Index=y? 11-4 Power Operation Index G-17 18Operation Index Index Index-1 Index-2 Index-3 EQN List TOP 6-7, F-2 Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Index-11 Angle between two vectors Index-12