Hp 33s User Manual

hp 33s scientific calculatoruser's guide HEdition 3 HP part number F2216-90001

8 Contents Selecting a Base Mode in a Program... 12–22Numbers Entered in Program Lines ... 12–23Polynom

6–8 Entering and Evaluating Equations To edit an equation you're typing: 1. Press b repeatedly until you delete the unwanted number or functio

Entering and Evaluating Equations 6–9Keys: Display: Description: |H/ºº 1!.2Shows the current equation in the equation list. bº 1!.2-

6–10 Entering and Evaluating Equations Because many equations have two sides separated by "=", the basic value of an equation is the differ

Entering and Evaluating Equations 6–11The evaluation of an equation takes no values from the stack — it uses only numbers in the equation and varia

6–12 Entering and Evaluating Equations a 6 q)Changes cubic millimeters to liters (but doesn't change V). Using XEQ for Evaluation If an e

Entering and Evaluating Equations 6–13To change the number, type the new number and press g. This new number writes over the old value in the X–r

6–14 Entering and Evaluating Equations Order Operation Example 1 Functions and Parentheses 1%-2,1%-22 Power (  )%:3 Unary Minus (^).4

Entering and Evaluating Equations 6–15Equation Functions The following table lists the functions that are valid in equations. Appendix G, "Ope

6–16 Entering and Evaluating Equations 01.%(.201%(1.&22Eleven of the equation functions have names that differ from their equivalent ope

Entering and Evaluating Equations 6–17Single letter nameNo implied multiplicationDivision is done before additionParentheses used to group items P=

Contents 915. Mathematics ProgramsVector Operations ...15–1Solutions of Simultaneous Equation

6–18 Entering and Evaluating Equations Syntax Errors The calculator doesn't check the syntax of an equation until you evaluate the equation and

Solving Equations 7–17Solving Equations In chapter 6 you saw how you can use  to find the value of the left–hand variable in an assignment–type equa

7–2 Solving Equations If the displayed value is the one you want, press g.If you want a different value, type or calculate the value and press g.(

Solving Equations 7–3/#º!-)ºº!:Terminates the equation and displays the left end. |//Checksum and length. g (acceleration due to

7–4 Solving Equations Example: Solving the Ideal Gas Law Equation.The Ideal Gas Law describes the relationship between pressure, volume, temperature,

Solving Equations 7–5g #O/)Stores 297.1 in T; solves for P in atmospheres. A 5–liter flask contains nitrogen gas. The pressure is 0.05 a

7–6 Solving Equations When SOLVE evaluates an equation, it does it the same way X does — any "=" in the equation is treated as a " – &q

Solving Equations 7–7Interrupting a SOLVE Calculation To halt a calculation, press  or g. The current best estimate of the root is in the unknown va

7–8 Solving Equations If an equation does not allow certain values for the unknown, guesses can prevent these values from occurring. For example,

Solving Equations 7–9Type in the equation: Keys: Display: Description: |HL V |d#/¾Selects Equation mode and starts the equation. |] 40 L H |`

10 Contents Resetting the Calculator ... B–2Clearing Memory ...

7–10 Solving Equations Keys: Display: Description: )This value from the Y–register is the estimate made just prior to the final result. Sinc

Solving Equations 7–11For More Information This chapter gives you instructions for solving for unknowns or roots over a wide range of applications. A

Integrating Equations 8–18Integrating Equations Many problems in mathematics, science, and engineering require calculating the definite integral of a

8–2 Integrating Equations Integrating Equations ( ³ FN)To integrate an equation: 1. If the equation that defines the integrand's function isn&ap

Integrating Equations 8–3Find the Bessel function for x–values of 2 and 3. Enter the expression that defines the integrand's function: cos (x si

8–4 Integrating Equations Now calculate J0(3) with the same limits of integration. You must respecify the limits of integration (0, π) since they were

Integrating Equations 8–5Keys: Display: Description: |H The current equation or  ! !Selects Equation mode. OL X 1%¾Starts the equation

8–6 Integrating Equations Specifying Accuracy The display format's setting (FIX, SCI, ENG, or ALL) determines the precision of the integration ca

Integrating Equations 8–7| X !!³/)The integral approximated to two decimal places. [).The uncertainty of the approximation of

Contents 11Underflow...D–14E. More about IntegrationHow the Integral Is Evaluated.

8–8 Integrating Equations  {})Restores Degrees mode. This uncertainty indicates that the result might be correct to only three decimal place

Operations with Complex Numbers 9–19Operations with Complex Numbers The HP 33s can use complex numbers in the form x + iy.It has operations for c

9–2 Operations with Complex Numbers Since the imaginary and real parts of a complex number are entered and stored separately, you can easily work wit

Operations with Complex Numbers 9–3Functions for One Complex Number, z To Calculate: Press: Change sign, –z {G^Inverse, 1/z {GNatural log, ln z {

9–4 Operations with Complex Numbers Examples: Here are some examples of trigonometry and arithmetic with complex numbers: Evaluate sin (2 + i 3)Keys:

Operations with Complex Numbers 9–5 2  3 ^.).)Enters imaginary part of second complex number as a fraction. 3{Gz.))Comp

9–6 Operations with Complex Numbers rreal(a, b)imaginaryθExample: Vector Addition.Add the following three loads. You will first need to convert the p

Operations with Complex Numbers 9–7{G).)Adds L1 + L2 + L3.{r))Converts vector back to polar form; displays r,θ

Base Conversions and Arithmetic 10–110Base Conversions and Arithmetic The BASE menu ( {x ) lets you change the number base used for entering number

10–2 Base Conversions and Arithmetic {x {}Base 2. {x {})Restores base 10; the original decimal value has been preserved, includi

Base Conversions and Arithmetic 10–3If the result of an operation cannot be represented in 36 bits, the display shows #$ and then shows the l

10–4 Base Conversions and Arithmetic The Representation of Numbers Although the display of a number is converted when the base is changed, its stored

Base Conversions and Arithmetic 10–5Range of Numbers The 36-bit word size determines the range of numbers that can be represented in hexadecimal (9

10–6 Base Conversions and Arithmetic Windows for Long Binary Numbers The longest binary number can have 36 digits — three times as many digits as fit

Statistical Operations 11–111Statistical Operations The statistics menus in the HP 33s provide functions to statistically analyze a set of one– or tw

11–2 Statistical Operations Entering One–Variable Data 1. Press {c {Σ} to clear existing statistical data. 2. Key in each x–value and press .3. The

Statistical Operations 11–31. Reenter the incorrect data, but instead of pressing , press {. This deletes the value(s) and decrements n.2. Enter

11–4 Statistical Operations Statistical Calculations Once you have entered your data, you can use the functions in the statistics menus. Statistics Me

Statistical Operations 11–515.5 9.25 10.012.5 12.0 8.5Calculate the mean of the times. (Treat all data as x–values.) Keys: Display: Description: {c

Part 1 Basic Operation

11–6 Statistical Operations Sample Standard Deviation Sample standard deviation is a measure of how dispersed the data values are about the mean sampl

Statistical Operations 11–7Example: Population Standard Deviation.Grandma Hinkle has four grown sons with heights of 170, 173, 174, and 180 cm. Find

11–8 Statistical Operations To find an estimated value for x (or y), key in a given hypothetical value for y(or x), then press | {ºˆ} (or | {¸ˆ}).

Statistical Operations 11–9x0 20 40 60 808.507.5 06.505.504.50r = 0.9880m = 0.0387b = 4.8560(70, y)yXWhat if 70 k

11–10 Statistical Operations Normalizing Close, Large Numbers The calculator might be unable to correctly calculate the standard deviation and linear

Statistical Operations 11–11If you've entered statistical data, you can see the contents of the statistics registers. Press{Y {#}, then use 

11–12 Statistical Operations Statistics Registers Register Number Description n 28 Number of accumulated data pairs. Σx 29 Sum of accumulated x–valu

Part 2 Programming

Simple Programming 12–112Simple Programming Part 1 of this manual introduced you to functions and operations that you can use manually, that is, by p

12–2 Simple Programming RPN mode ALG mode ººπ º º π  !This very simple program assumes that the value for

Simple Programming 12–3Designing a Program The following topics show what instructions you can put in a program. What you put in a program affects ho

12–4 Simple Programming When a program finishes running, the last RTN instruction returns the program pointer to  !, the top of program memory.

Simple Programming 12–5For output, you can display a variable with the VIEW instruction, you can display a message derived from an equation, or you c

12–6 Simple Programming 5. End the program with a return instruction, which sets the program pointer back to ! after the program runs. Press |

Simple Programming 12–7Function Names in Programs The name of a function that is used in a program line is not necessarily the same as the function&a

12–8 Simple Programming Example: Entering a Program with an Equation.The following program calculates the area of a circle using an equation, rather t

Simple Programming 12–9Running a Program To run or execute a program, program entry cannot be active (no program–line numbers displayed; PRGM off). P

12–10 Simple Programming 2. Press {Vlabel to set the program pointer to the start of the program (that is, at its LBL instruction). The ! instructio

Simple Programming 12–11Entering and Displaying Data The calculator's variables are used to store data input, intermediate results, and final re

Getting Started 1–11Getting Started vWatch for this symbol in the margin. It identifies examples or keystrokes that are shown in RPN mode and must be

12–12 Simple Programming Pressg(run/stop) to resume the program. The value you keyed in then writes over the contents of the X–register and is stored

Simple Programming 12–13For example, see the "Coordinate Transformations" program in chapter 15. Routine D collects all the necessary input

12–14 Simple Programming Pressing {c clears the contents of the displayed variable. Pressg to continue the program, If you don't want the pro

Simple Programming 12–15V = πR2HS = 2π R2 + 2π RH = 2π R ( R + H )Keys: (In RPN mode) Display: Description: {e{V!Program, entry; sets poin

12–16 Simple Programming Keys: (In RPN mode) Display: Description: | V  #$ #Displays volume. | S  #$ Displays surface area. |

Simple Programming 12–17The display is cleared by other display operations, and by the RND operation if flag 7 is set (rounding to a fraction). Press

12–18 Simple Programming To see the line in the program containing the error–causing instruction, press {e. The program will have stopped at that poin

Simple Programming 12–192. Press b. This turns on the "¾" editing cursor, but does not delete anything in the equation. 3. Press b as requi

12–20 Simple Programming Memory Usage If during program entry you encounter the message & ", then there is not enough room in program

Simple Programming 12–21To clear all programs from memory: 1. Press {e to display program lines (PRGM annunciator on). 2. Press {c {} to clear pro

1–2 Getting Started Highlights of the Keyboard and Display Shifted Keys Each key has three functions: one printed on its face, a left–shifted function

12–22 Simple Programming Nonprogrammable Functions The following functions of the HP 33s are not programmable: {c {}{V{c {}{Vlabel nnnnb{Y,

Simple Programming 12–23Numbers Entered in Program Lines Before starting program entry, set the base mode. The current setting for the base mode dete

12–24 Simple Programming Keys: (In ALG mode) Display: Description: {e{V!{ A  { X"!%55zºL X

Simple Programming 12–25A more general form of this program for any equation Ax4+ Bx3+ Cx2+ Dx + E would be: "!

Programming Techniques 13–113Programming Techniques Chapter 12 covered the basics of programming. This chapter explores more sophisticated but useful

13–2 Programming Techniques Calling Subroutines (XEQ, RTN) A subroutine is a routine that is called from (executed by) another routine and returns to

Programming Techniques 13–3Nested Subroutines A subroutine can call another subroutine, and that subroutine can call yet another subroutine. This &qu

13–4 Programming Techniques In RPN mode,   Starts subroutine here.  "! Enters A.  "! Enters B.  "! En

Programming Techniques 13–5A Programmed GTO Instruction The GTO label instruction (press {Vlabel) transfers the execution of a running program to the

Getting Started 1–3Pressing { or | turns on the corresponding ¡ or ¢annunciator symbol at the top of the display. The annunciator remains on until yo

13–6 Programming Techniques To  !:{V.To a line number: {Vlabel nnnn (nnnn < 10000). For example, {V A0005. To a label: {V label —bu

Programming Techniques 13–7Flag tests. These check the status of flags, which can be either set or clear. Loop counters. These are usually used t

13–8 Programming Techniques Example: The "Normal and Inverse–Normal Distributions" program in chapter 16 uses the x<y? conditional in rou

Programming Techniques 13–9Flags 0, 1, 2, 3, and 4 have no preassigned meanings. That is, their states will mean whatever you define them to mean i

13–10 Programming Techniques Flag 10 controls program execution of equations: When flag 10 is clear (the default state), equations in running prog

Programming Techniques 13–11Annunciators for Set Flags Flags 0, 1, 2, 3 and 4 have annunciators in the display that turn on when the corresponding fl

13–12 Programming Techniques Example: Using Flags.The "Curve Fitting" program in chapter 16 uses flags 0 and 1 to determine whether to take

Programming Techniques 13–13Program Lines: (In RPN mode) Description: ...    Clears flag 0, the indicator for In X.    Clears flag 1,

13–14 Programming Techniques Example: Controlling the Fraction Display.The following program lets you exercise the calculator's fraction–display

Programming Techniques 13–15Program Lines: (In ALG mode) Description:   Begins the fraction program.   Clears three fraction flags.

NoticeREGISTER YOUR PRODUCT AT: www.register.hp.comTHIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOU

1–4 Getting Started Silver Paint Keys Those eight silver paint keys have their specific pressure points marked in blue position in the illustration be

13–16 Programming Techniques Use the above program to see the different forms of fraction display: Keys: (In ALG mode) Display: Description: X F #@v

Programming Techniques 13–17This routine (taken from the "Coordinate Transformations" program on page 15–32 in chapter 15) is an example of

13–18 Programming Techniques Loops with Counters (DSE, ISG) When you want to execute a loop a specific number of times, use the {l(increment; skip if

Programming Techniques 13–19Given the loop–control number ccccccc.fffii, ISG increments ccccccc to ccccccc + ii, compares the new ccccccc with fff, a

13–20 Programming Techniques Indirectly Addressing Variables and Labels Indirect addressing is a technique used in advanced programming to specify a v

Programming Techniques 13–21The Indirect Address, (i) Many functions that use A through Z (as variables or labels) can use  to refer to A through Z

13–22 Programming Techniques STO(i)RCL(i)STO +, –,× ,÷, (i)RCL +, –,× ,÷, (i)XEQ(i)GTO(i)X<>(i)INPUT(i)VIEW(i)DSE(i)ISG(i)SOLVE(i)³FN d(i)FN=(i)

Programming Techniques 13–23& & !- L& %11L22If i holds: Then XEQ(i) calls: To: 1 LBL A Compute yˆ for straight–line

13–24 Programming Techniques Program Lines: (In RPN mode) Description:    This routine collects all known values in three equations.  

Programming Techniques 13–25Program Lines: (In RPN mode) Description:   Begins the program.   Sets equations for execution.  

Getting Started 1–5Keys for Clearing Key Description bBackspace.Keyboard–entry mode: Erases the character immediately to the left of "_"

Solving and Integrating Programs 14–114Solving and Integrating Programs Solving a Program In chapter 7 you saw how you can enter an equation — it&a

14–2 Solving and Integrating Programs 2. Include an INPUT instruction for each variable, including the unknown. INPUT instructions enable you to solv

Solving and Integrating Programs 14–3R = The universal gas constant (0.0821 liter–atm/mole–K or 8.314 J/mole–K). T = Temperature (kelvins;

14–4 Solving and Integrating Programs Keys: (In ALG mode) Display: Description: |WGSelects "G" — the program. SOLVE evaluates to find th

Solving and Integrating Programs 14–5| !Ends the program. )Cancels Program–entry mode. Checksum and length of program: 36FF 21 N

14–6 Solving and Integrating Programs Using SOLVE in a Program You can use the SOLVE operation as part of a program. If appropriate, include or promp

Solving and Integrating Programs 14–7Program Lines: (In RPN mode) Description: %  % Setup for X.%  Index for X.% !  Branches t

14–8 Solving and Integrating Programs 2. Select the program that defines the function to integrate: press |Wlabel. (You can skip this step if you&ap

Solving and Integrating Programs 14–9Example: Program Using Equation.The sine integral function in the example in chapter 8 is³=t0dx(Si(t) )xxsinTh

1–6 Getting Started Keys for Clearing (continued)Key Description {cThe CLEAR menu ({º} {# } {} {´}) Contains options for clearing x (the number

14–10 Solving and Integrating Programs ³ GvariableThe programmed³FN instruction does not produce a labeled display (³= value)since this might not b

Solving and Integrating Programs 14–11Restrictions on Solving and Integrating The SOLVE variable and ³FN d variable instructions cannot call a rout

Mathematics Programs 15–115Mathematics Programs Vector Operations This program performs the basic vector operations of addition, subtraction, cross p

15–2 Mathematics Programs Vector addition and subtraction: v1 + v2 = (X + U)i + (Y + V)j + (Z + W)kv2 – v1 = (U – X)i + (V – Y)j + (W – Z)kCross produ

Mathematics Programs 15–3Program Listing: Program Lines: (In ALG mode) Description   Defines the beginning of the rectangular input/displa

15–4 Mathematics Programs Program Lines: (In ALG mode) Description  ! 'Stores Z = R cos(P).  !º65¸θ8T´¸8ºCalculate

Mathematics Programs 15–5Program Lines: (In ALG mode) Description   % - " ! %Saves X + U in X.  # - &

15–6 Mathematics Programs Program Lines: (In ALG mode) Description  !Calculates (ZU – WX), which is the Y component.  !   %

Mathematics Programs 15–7Program Lines: (In ALG mode) Description   $ ¸8º´θ8TCalculates the magnitude of the U, V, W vector.  !

Getting Started 1–7Using Menus There is a lot more power to the HP 33s than what you see on the keyboard. This is because 14 of the keys are menu key

15–8 Mathematics Programs 3. Key in R and press g, key in T and press g, then key in P and press g. Continue at step 5. 4. Key in X and press g, key i

Mathematics Programs 15–9N(y)SWE(x)AntennaTransmitter7.315.7Keys: (In ALG mode) Display: Description:  {}Sets Degrees mode. X R%@valueStarts

15–10 Mathematics Programs ZXY125o63oF = 17 T = P = 171215ooF = 23 T = 80 P = 742oo1.07mFirst, add the force vectors. Keys: (In ALG mode) Display:

Mathematics Programs 15–11g@)Displays P of resultant vector. X E @)Enters resultant vector. Since the moment equals the cross produ

15–12 Mathematics Programs 125g@)Sets T equal to 125. 63g@)Sets P equal to 63. X D /)Calculates dot product. g/)Ca

Mathematics Programs 15–13Program Listing: Program Lines: (In RPN mode) Description   Starting point for input of coefficients.  )

15–14 Mathematics Programs Program Lines: (In RPN mode) Description  º  . ! 'Calculates H'× determinant = BG – AH. 

Mathematics Programs 15–15Program Lines: (In RPN mode) Description    º    º  . ! Calculates G&

15–16 Mathematics Programs Program Lines: (In RPN mode) Description row. %  Sets index value to point to last element in third row. Ch

Mathematics Programs 15–17Program Lines: (In RPN mode) Description  º  º Calculates A×E×I.   º  º 

1–8 Getting Started HP 33s Menus (continued)Menu Name Menu Description Chapter Other functions MEM# Memory status (bytes of memory available); ca

15–18 Mathematics Programs Program Instructions: 1. Key in the program routines; press  when done. 2. Press X A to input coefficients of matrix and

Mathematics Programs 15–19Keys: (In RPN mode) Display: Description: X A @valueStarts input routine. 23g@valueSets first coefficient, A, equal

15–20 Mathematics Programs g@.)Displays next value. g@)Displays next value. g@)Displays next value. X I )Inverts inverse

Mathematics Programs 15–21b0 = a0(4a2 – a32) – a12.Lety0 be the largest real root of the above cubic. Then the fourth–order polynomial is reduced to

15–22 Mathematics Programs Program Listing: Program Lines: (In RPN mode) Description   Defines the beginning of the polynomial root finder r

Mathematics Programs 15–23Program Lines: (In RPN mode) Description    ! %First initial guess.  -+.Second initial guess.  

15–24 Mathematics Programs Program Lines: (In RPN mode) Description  !Checksum and length: B9A7 81   Starts second–order solution

Mathematics Programs 15–25Program Lines: (In RPN mode) Description Checksum and length: C7A6 51   Starts fourth–order solution routine.

15–26 Mathematics Programs Program Lines: (In RPN mode) Description   @ Complex roots? ! Calculate four roots of remaining fourth–ord

Mathematics Programs 15–27Program Lines: (In RPN mode) Description  ! Stores 1 or JK – a1/2.    !ª Calculates sign of C.

Getting Started 1–9Example:6÷ 7 = 0.8571428571… Keys: Display: 6 7 q%    ({}) ( or  ) ).Menus help you

15–28 Mathematics Programs Program Lines: (In RPN mode) Description  ! "Displays complex roots if any.  ! %Stores second real roo

Mathematics Programs 15–29Because of round–off error in numerical computations, the program may produce values that are not true roots of the polynom

15–30 Mathematics Programs A through E Coefficients of polynomial; scratch. F Order of polynomial; scratch. G Scratch.H Pointer to polynomial coeffic

Mathematics Programs 15–31Example 2: Find the roots of 4x4 – 8x3 – 13x2– 10x + 22 = 0. Because the coefficient of the highest–order term must be 1, d

15–32 Mathematics Programs Example 3: Find the roots of the following quadratic polynomial: x2+ x – 6 = 0 Keys: (In RPN mode) Display: Description: X

Mathematics Programs 15–33yy'xx'[]m, nNew coordinatesystemOld coordinatesystem[0, 0]xPuyvθ

15–34 Mathematics Programs Program Listing: Program Lines: (In RPN mode) Description   This routine defines the new coordinate system. 

Mathematics Programs 15–35Program Lines: (In RPN mode) Description  "! #Prompts for and stores V.  "Pushes V up and recal

15–36 Mathematics Programs 7. Press X N to start the old–to–new transformation routine. 8. Key in X and press g.9. Key in Y, press g, and see the x–

Mathematics Programs 15–37yy'xP3(6, 8)P1 (_9, 7)P2 (_5, _4)P'4(2.7, _3.6)(, ) = (7, _4) T = 27MNo(M, N)TKeys: (In RPN mode) Display:

1–10 Getting Started RPN and ALG Keys The calculator can be set to perform arithmetic operations in either RPN (Reverse Polish Notation) or ALG (Algeb

15–38 Mathematics Programs g%@.)Resumes the old–to–new routine for next problem. 5^g&@)Stores –5 in X.4^g"/.)Stores –4

Statistics Programs 16–116Statistics Programs Curve Fitting This program can be used to fit one of four models of equations to your data. These model

16–2 Statistics Programs yxy B Mx=+Straight Line FitSyxy Be Mx=Exponential Curve FitEyxy B MIn x=+Logarithmic Curve FitLyxy BxM=Power Curve Fi

Statistics Programs 16–3Program Listing: Program Lines: (In RPN mode) Description   This routine sets, the status for the straight–line mod

16–4 Statistics Programs Program Lines: (In RPN mode) Description ' Sets the loop counter to zero for the first input. Checksum and length:

Statistics Programs 16–5Program Lines: (In RPN mode) Description  ! Stores b in B. #$ Displays value.  PCalculates coefficient

16–6 Statistics Programs Program Lines: (In RPN mode) Description   %  º  - Calculates yˆ = M In X + B. !Re

Statistics Programs 16–7Program Lines: (In RPN mode) Description !!!¸%!º!Calculates Y= B(XM). !!Returns to the calli

16–8 Statistics Programs 5. Repeat steps 3 and 4 for each data pair. If you discover that you have made an error after you have pressed gin step 3 (w

Statistics Programs 16–9Example 1: Fit a straight line to the data below. Make an intentional error when keying in the third data pair and correct it

Getting Started 1–11The Display and Annunciators First LineSecond LineAnnunciatorsThe display comprises two lines and annunciators.The first line can

16–10 Statistics Programs 100g%@)Enters y–value of data pair. 36.2g&@)Enters x–value of data pair. 97.5g%@)Enters y–value o

Statistics Programs 16–11 Logarithmic Exponential Power To start: X L X E X P R 0.9965 0.9945 0.9959 M –139.0088 51.1312 8.9730 B 65.8446 0.0177

16–12 Statistics Programs Program Listing: Program Lines: (In RPN mode) Description   This routine initializes the normal distribution progr

Statistics Programs 16–13Program Lines: (In RPN mode) Description ! !- %Adds the correction to yield a new Xguess.!  ! )!

16–14 Statistics Programs Program Lines: (In RPN mode) Description  ª  º  ª -+. H% !Returns to the c

Statistics Programs 16–156. To calculate Q(X) given X,X D. 7. After the prompt, key in the value of X and press g. The result, Q(X), is displayed. 8

16–16 Statistics Programs X D %@valueStarts the distribution program and prompts for X.3g/)Enters 3 for X and starts computation of Q(X). Di

Statistics Programs 16–1755g @)Stores 55 for the mean. 15.3g)Stores 15.3 for the standard deviation. X D %@valueStarts the distributi

16–18 Statistics Programs Program Listing: Program Lines: (In ALG mode) Description  Start grouped standard deviation program. ;Cl

Statistics Programs 16–19Program Lines: (In ALG mode) Description  !-1L2Updates ¦iifx2 in register 31.  !-Increments (

1–12 Getting Started HP 33s Annunciators Annunciator Meaning Chapter £The "£(Busy)" annunciator blinks while an operation, equation, or p

16–20 Statistics Programs Program Instructions: 1. Key in the program routines; press  when done. 2. Press X S to start entering new data. 3. Key in

Statistics Programs 16–21Group 1 2 3 4 5 6xi5 8 13 15 22 37fi17 26 37 43 73 115Keys: (In ALG mode) Display: Description: X S %@valuePrompts for t

16–22 Statistics Programs g%@)Prompts for the fourth xi.15g@)Prompts for the fourth fi.43g/)Displays the counter. g%@)

Miscellaneous Programs and Equations 17–117Miscellaneous Programs and Equations Time Value of Money Given any four of the five values in the "

17–2 Miscellaneous Programs and Equations Equation Entry: Key in this equation: ºº1.1-ª2:.2ª-º1-ª2:.-Keys: (In RPN mode) Display

Miscellaneous Programs and Equations 17–3SOLVE instructions: 1. If your first TVM calculation is to solve for interest rate, I, press 1 I I. 2. Pre

17–4 Miscellaneous Programs and Equations B = 7,250 _ 1,500I = 10.5% per year N = 36 monthsF = 0P = ?Keys: (In RPN mode) Display: Description:  {

Miscellaneous Programs and Equations 17–5Part 2. What interest rate would reduce the monthly payment by $10?Keys: (In RPN mode) Display: Descripti

17–6 Miscellaneous Programs and Equations g@)Retains P; prompts for I.g@)Retains 0.56 in I; prompts for N. 24g@8)Stores 24 in N

Miscellaneous Programs and Equations 17–7LBL YVIEW PrimeLBL ZP + 2 x→LBL Px P3 D→→LBL Xx = 0?yesnoStartnoyesNote: x is the value

Getting Started 1–13HP 33s Annunciators (continued)Annunciator Meaning Chapter §,¨The  or  keys are active to scroll the display, i.e. there are

17–8 Miscellaneous Programs and Equations Program Listing: Program Lines: (In ALG mode) Description &  &This routine displays prime n

Miscellaneous Programs and Equations 17–9Program Lines: (In ALG mode) Description %  % º>¸@Tests to see whether all possible facto

17–10 Miscellaneous Programs and Equations Keys: (In ALG mode) Display: Description: 789X P /)Calculates next prime number after 789. g/

Part 3 Appendixes and Reference

Support, Batteries, and Service A–1ASupport, Batteries, and Service Calculator Support You can obtain answers to questions about using your calcula

A–2 Support, Batteries, and Service A: You must clear a portion of memory before proceeding. (See appendix B.) Q: Why does calculating the sine (or t

Support, Batteries, and Service A–3Once you've removed the batteries, replace them within 2 minutes to avoid losing stored information. (Have

A–4 Support, Batteries, and Service Warning Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing

Support, Batteries, and Service A–5If the calculator responds to keystrokes but you suspect that it is malfunctioning: 1. Do the self–test descr

Contents 1ContentsPart 1. Basic Operation1. Getting StartedImportant Preliminaries...1–1Turning

1–14 Getting Started Keying in Numbers You can key in a number that has up to 12 digits plus a 3–digit exponent up to ±499. If you try to key in a num

A–6 Support, Batteries, and Service Warranty HP 33s Scientific Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer,

Support, Batteries, and Service A–77. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REME

A–8 Support, Batteries, and Service Norway +47-63849309 Portugal +351-229570200 Spain +34-915-642095 Sweden +46-851992065 Switzerland +41-1-4

Support, Batteries, and Service A–9N.America Country : Telephone numbers USA 1800-HP INVENT Canada (905)206-4663 or 800-HP INVENT ROTC = Rest

A–10 Support, Batteries, and Service File name 33s-English-Manual-050427-Publication(Edition 3) Page : 387 Printed Date : 2005/4/27

User Memory and the Stack B–1BUser Memory and the Stack This appendix covers The allocation and requirements of user memory, How to reset the c

B–2 User Memory and the Stack 2. If necessary, scroll through the equation list (press  or  ) until you see the desired equation. 3. Press | to s

User Memory and the Stack B–3Clearing Memory The usual way to clear user memory is to press {c {}. However, there is also a more powerful cleari

B–4 User Memory and the Stack Memory may inadvertently be cleared if the calculator is dropped or if power is interrupted. The Status of Stack Lift T

User Memory and the Stack B–5DEG, RAD, GRAD FIX, SCI, ENG, ALL DEC, HEX, OCT, BIN CLVARS PSE SHOW RADIX . RADIX , CLΣg and STOP and * and

Getting Started 1–15Keying in Exponents of Ten Use a (exponent) to key in numbers multiplied by powers of ten. For example, take Planck's consta

B–6 User Memory and the Stack File name 33s-English-Manual-041129-Publication(Edition 3) Page : 388 Printed Date : 2004/12/8 Size :

ALG: Summary C–1CALG: Summary About ALG This appendix summarizes some features unique to ALG mode, including, Two–number arithmetic Chain calcu

C–2 ALG: Summary Doing Two–number Arithmetic in ALG This discussion of arithmetic using ALG replaces the following parts that are affected by ALG mode

ALG: Summary C–3To Calculate: Press: Display: 123 12  3 :/8)641/3 (cube root) 3  64 º/)Percentage Calculations The Pe

C–4 ALG: Summary Example: Suppose that the $15.76 item cost $16.12 last year. What is the percentage change from last year's price to this year&a

ALG: Summary C–5 File name hp 33s_user's manual_English_E_HDPM20PIE30.doc Page : 409 Printed Date : 2005/10/17 Size : 13

C–6 ALG: Summary 750z12q360or750z12q360In the second case, the qkey acts like the key by displaying the result of 750 × 12. Here’s a longer chain

ALG: Summary C–7You can press  or  (or and |) to review the entire contents of the stack and recall them. However, in normal operation in ALG

C–8 ALG: Summary 8´¸8º&/)Displays y.If you want to perform a coordinate conversion as part of a chain calculation, you need to use pa

ALG: Summary C–9Operations with Complex Numbers To enter a complex number웛x + iy.1. Type the real part, x, then the function key. 2. Type the imagi

1–16 Getting Started Keys: Display: Description: 123_ Digit entry not terminated: the number is not complete. If you execute a function to calcul

C–10 ALG: Summary Examples: Evaluate sin (2워3i )Keys: Display: Description: |]23{G|`1워L2/)O 1워L2/) 1워L2/.)

ALG: Summary C–11 File name hp 33s_user's manual_English_E_HDPM20PIE30.doc Page : 409 Printed Date : 2005/10/18 Size : 1

C–12 ALG: Summary File name hp 33s_user's manual_English_E_HDPM20PIE30.doc Page: 409 Printed Date : 2005/10/18 Size : 13.7 x

ALG: Summary C–13Keys: Display: Description: {c {´}Clears existing statistical data. 4[ 20 8Q/)Enters the first new data pair. 6[ 400 

More about Solving D–1DMore about Solving This appendix provides information about the SOLVE operation beyond that given in chapter 7. How SOLVE Fi

D–2 More about Solving f (x)xaf (x)bxf (x)xcf (x)xdFunction Whose Roots Can Be Found In most situations, the calculated root is an accurate estimate

More about Solving D–3Interpreting Results The SOLVE operation will produce a solution under either of the following conditions: If it finds an e

D–4 More about Solving Keys: Display: Description: |HSelect Equation mode. 2^zL X  3 4zL X 2 6 zLX 8 .º%:-º%:.ºEnters the

More about Solving D–5|//Checksum and length. Cancels Equation mode. Now, solve the equation to find its positive and negative roots:

Getting Started 1–17One–Number Functions To use a one–number function (such as ,#,!,{ @,{$,|K,{ ,Q or ^)1. Key in the number. ( You don't

D–6 More about Solving f (x)xaf (x)xbSpecial Case: A Discontinuity and a PoleExample: Discontinuous Function.Find the root of the equation: IP(x) = 1

More about Solving D–7 X #%/)Finds a root with guesses 0 and 5.|)Shows root, to 11 decimal places. |)Th

D–8 More about Solving Now, solve to find the root. Keys: Display: Description: 2.3I X 2.7)_Your initial guesses for the root.|H%ª1%:.2.S

More about Solving D–9f (x)xaf (x)xbf (x)xcCase Where No Root Is FoundExample: A Relative Minimum.Calculate the root of this parabolic equation: x2

D–10 More about Solving Cancels Equation mode. Now, solve to find the root: Keys: Display: Description: 0I X 10_Your initial guesses for the

More about Solving D–11 )Previous estimate is the same. |)f (x) = 0 Watch what happens when you use negative values for guesse

D–12 More about Solving Now attempt to find a negative root by entering guesses 0 and –10. Notice that the function is undefined for values of x betw

More about Solving D–13 ¶ !Checksum and length: B956 75 You can subsequently delete line J0003 to save memory. Solve for X using

D–14 More about Solving Underflow Underflow occurs when the magnitude of a number is smaller than the calculator can represent, so it substitutes zer

More about Integration E–1EMore about Integration This appendix provides information about integration beyond that given in chapter 8.How the Integ

1–18 Getting Started For example, To calculate: Press: Display: 12 + 3 12  3 )12 – 3 12  3 )12× 3 12  3 z)123 12  3 8

E–2 More about Integration As explained in chapter 8, the uncertainty of the final approximation is a number derived from the display format, which s

More about Integration E–3f (x)xWith this number of sample points, the algorithm will calculate the same approximation for the integral of any of t

E–4 More about Integration Keys: Display: Description: |HSelect equation mode. L X z%º%1¾Enter the equation. L X |`%º%1.%2End of the equ

More about Integration E–5f (x)xThe graph is a spike very close to the origin. Because no sample point happened to discover the spike, the algorith

E–6 More about Integration Note that the rapidity of variation in the function (or its low–order derivatives) must be determined with respect to the

More about Integration E–7In many cases you will be familiar enough with the function you want to integrate that you will know whether the function

E–8 More about Integration [).Uncertainty of approximation. This is the correct answer, but it took a very long time. To understand why, compa

More about Integration E–9Because the calculation time depends on how soon a certain density of sample points is achieved in the region where the f

Messages F–1FMessagesThe calculator responds to certain conditions or keystrokes by displaying a message. The ¤ symbol comes on to call your attentio

Getting Started 1–19Number of Decimal Places All numbers are stored with 12–digit precision, but you can select the number of decimal places to be di

F–2 Messages File name 33s-English-Manual-041129-Publication(Edition 3) Page : 388 Printed Date : 2004/12/8 Size : 13.7 x 21.2 cm 

Messages F–3% !!Attempted to refer to a nonexistent program label (or line number) with V,V,X, or {}.Note that the error % !! can m

F–4 Messages #The calculator is solving an equation or program for its root. This might take a while. !12Attempted to calculate the squa

Operation Index G–1GOperation Index This section is a quick reference for all functions and operations and their formulas, where appropriate. The lis

G–2 Operation Index Name Keys and Description Page ¼Displays previous entry in catalog; moves to previous equation in equation list; moves program

Operation Index G–3Name Keys and Description Page ¼Σ+ Accumulates (y, x) into statistics registers. 11–2 Σ–{ Removes (y, x) from statistics reg

G–4 Operation Index Name Keys and Description Page ¼³FN d variable| { ³ G _} variableIntegrates the displayed equation or the program selected b

Operation Index G–5Name Keys and Description Page ¼ASINH {{MHyperbolic arc sine.Returns sinh –1x.4–6 1 ATAN{SArc tangent.Returns tan –1x.4–4 1 A

G–6 Operation Index Name Keys and Description Page ¼{c Displays menu to clear numbers or parts of memory; clears indicated variable or program fro

Operation Index G–7Name Keys and Description Page ¼CMPLX ×{GzComplex multiplication.Returns (z1x + i z1y)× (z2x + i z2y). 9–2 CMPLX ÷{GqComplex d

1–20 Getting Started Engineering Format ({}) ENG format displays a number in a manner similar to scientific notation, except that the exponent is a

G–8 Operation Index Name Keys and Description Page ¼COSH{RHyperbolic cosine. Returns cosh x.4–6 1 | Functions to use 40 physics constants.4–8

Operation Index G–9Name Keys and Description Page ¼ Separates two numbers keyed in sequentially; completes equation entry; evaluates the display

G–10 Operation Index Name Keys and Description Page ¼FS?n|y { @} nIf flag n (n = 0 through 11) is set, executes the next program line; if flag n i

Operation Index G–11Name Keys and Description Page ¼(i)LIIndirect. Value of variable whose letter corresponds to the numeric value stored in var

G–12 Operation Index Name Keys and Description Page ¼KG{} Converts pounds to kilograms. 4–13 1 L{ Converts gallons to liters.4–13 1 LASTx{Ret

Operation Index G–13Name Keys and Description Page ¼OCT {x {!}Selects Octal (base 8) mode. 10–1 | Turns the calculator off. 1–1 Pn,r{_Perm

G–14 Operation Index Name Keys and Description Page ¼RCL variableLvariableRecall.Copies variable into the X–register. 3–5 RCL+ variableLvariableR

Operation Index G–15Name Keys and Description Page ¼Rµ|Roll up.Moves t to the X–register, z to the T–register, y to the Z–register, and x to the

G–16 Operation Index Name Keys and Description Page ¼pg Inserts a blank space character during equation entry. 13–14 2 SQ!Square of argument. 6–15

Operation Index G–17Name Keys and Description Page ¼TAN UTangent. Returns tan x. 4–3 1 TANH {UHyperbolic tangent.Returns tanh x.4–6 1 VIEW variab

Getting Started 1–21For example, in the number 14.8745632019, you see only "14.8746" when the display mode is set to FIX 4, but the last si

G–18 Operation Index Name Keys and Description Page ¼xw Returns weighted mean of xvalues: (Σyixi)÷Σyi.11–4 1 | Displays the mean (arithmetic ave

Operation Index G–19Name Keys and Description Page ¼x≠0?|o {≠}If x≠0, executes next program line;if x=0, skips the next program line.13–7 x≤0?|o

G–20 Operation Index Name Keys and Description Page ¼yxPower.Returns y raised to the xthpower.4–2 1 Notes: 1. Function can be used in equations.

Index–1 File name 33s-English-Manual-050502-Publication(Edition 3) Page : 388 Printed Date : 2005/5/2 Size : 13.7 x 21.2 cm Inde

Index–2asymptotes of functions, D–8 Bbackspace key canceling VIEW, 3–3 clearing messages, 1–5, F–1 clearing X–register, 2–2, 2–6 deleting program line

Index–3program, 1–24, 12–20 using, 1–24 variable, 1–24, 3–3 chain calculations, 2–11 change–percentage functions, 4–6 changing sign of numbers, 1–14,

Index–4adjusting contrast, 1–1 annunciators, 1–11 function names in, 4–17 X–register shown, 2–2 display format affects integration, 8–2, 8–5, 8–7 affe

Index–5functions, 6–5, 6–15, G–1 in programs, 12–4, 12–6, 12–21, 13–10 integrating, 8–2 lengths, 6–18, 12–6, B–2 list of. See equation list long, 6–7

Index–6fractional–part function, 4–16 Fraction–display mode affects rounding, 5–7 affects VIEW, 12–13 setting, 1–23, 5–1, A–2 fractions accuracy indic

Index–7imaginary part (complex numbers), 9–1, 9–2 indirect addressing, 13–20, 13–21, 13–22 INPUT always prompts, 13–10 entering program data, 12–11 i

1–22 Getting Started 2. Key in the fraction numerator and press  again. The second separates the numerator from the denominator. 3. Key in the deno

Index–8order of calculation, 2–13 real–number, 4–1 stack operation, 2–4, 9–1 matrix inversion, 15–12 maximum of function, D–8 mean menu, 11–4 means (s

Index–9internal representation, 1–19, 10–4 large and small, 1–14, 1–16 limitations, 1–14 mantissa, 1–15 negative, 1–14, 9–3, 10–4 order in calculatio

Index–10checksums, 12–21 clearing, 12–5 duplicate, 12–5 entering, 12–3, 12–5 executing, 12–9 indirect addressing, 13–20, 13–21, 13–22 moving to, 12–10

Index–11testing, 12–9 using integration, 14–9 using SOLVE, 14–6 variables in, 12–11, 14–1, 14–7 prompts affect stack, 6–13, 12–12 clearing, 1–5, 6–13

Index–12 File name 33s-English-Manual-050502-Publication(Edition 3) Page : 388 Printed Date : 2005/5/2 Size : 13.7 x 21.2 cm SOLVE,

Index–13effect of , 2–5equation usage, 6–11 exchanging with variables, 3–6 exchanging X and Y, 2–4 filling with constant, 2–6 long calculations, 2–1

Index–14time value of money, 17–1 transforming coordinates, 15–32 T–register, 2–4 trigonometric functions, 4–4, 9–3 troubleshooting, A–4, A–5 turning

Index–15clearing in programs, 12–6 displayed, 2–2 during programs pause, 12–17 exchanging with variables, 3–6 exchanging with Y, 2–4 not clearing, 2–

Getting Started 1–23Displaying Fractions Press { to switch between Fraction–display mode and the current decimal display mode. Keys: Display: Des

2 Contents Periods and Commas in Numbers... 1–18Number of Decimal Places ... 1–19SH

1–24 Getting Started Calculator Memory The HP 33s has 31KB of memory in which you can store any combination of data (variables, equations, or program

RPN: The Automatic Memory Stack 2–12RPN: The Automatic Memory Stack This chapter explains how calculations take place in the automatic memory stack

2–2 RPN: The Automatic Memory Stack T0.0000 "Oldest" numberZYXDisplayed 0.00000.00000.0000Displayed The most "recent" number is

RPN: The Automatic Memory Stack 2–3Reviewing the Stack R¶ (Roll Down) The (roll down) key lets you review the entire contents of the stack by &q

2–4 RPN: The Automatic Memory Stack Exchanging the X– and Y–Registers in the Stack Another key that manipulates the stack contents is [ (x exchange y

RPN: The Automatic Memory Stack 2–53. The stack drops. Notice that when the stack lifts, it replaces the contents of the T– (top) register with

2–6 RPN: The Automatic Memory Stack Using a Number Twice in a Row You can use the replicating feature of  to other advantages. To add a number to it

RPN: The Automatic Memory Stack 2–7During program entry, b deletes the currently–displayed program line and  cancels program entry. During dig

2–8 RPN: The Automatic Memory Stack 2. Reusing a number in a calculation. See appendix B for a comprehensive list of the functions that save x in the

RPN: The Automatic Memory Stack 2–9Example: Suppose you made a mistake while calculating 16× 19 = 304 There are three kinds of mistakes you could h

Contents 33. Storing Data into VariablesStoring and Recalling Numbers...3–2Viewing a Variable without Recall

2–10 RPN: The Automatic Memory Stack TtttZzzt96.704Y96.704096.7040 zX96.704052.3947 52.3 947 149.0987 LASTXll52.3947TttZztY149.0987 zX52.39472.845

RPN: The Automatic Memory Stack 2–119.5a 15 )_Speed of light, c.z)Meters to R. Centaurus. 8.7{)Retrieves c.z)Mete

2–12 RPN: The Automatic Memory Stack Now study the following examples. Remember that you need to press only to separate sequentially–entered numbers

RPN: The Automatic Memory Stack 2–13Exercises Calculate: 0000.18105.0)53805.16(=xSolution: 16.3805 5 z# .05 qCalculate: 5743.21)]98()76[()]54()32[

2–14 RPN: The Automatic Memory Stack This method takes one additional keystroke. Notice that the first intermediate result is still the innermost par

RPN: The Automatic Memory Stack 2–15A Solution: 14 12  18  12 z 9  7 qCalculate: 232 – (13 × 9) + 1/7 = 412.1429 A Solution: 23! 13  9 z 7

Storing Data into Variables 3–13Storing Data into Variables The HP 33s has 31KB of user memory: memory that you can use to store numbers, equations

3–2 Storing Data into Variables Each black letter is associated with a key and a unique variable. The letter keys are automatically active when neede

Storing Data into Variables 3–3Viewing a Variable without Recalling It The | function shows you the contents of a variable without putting that nu

4 Contents Factorial ... 4–14Gamma...

3–4 Storing Data into Variables Clearing Variables Variables' values are retained by Continuous Memory until you replace them or clear them. Cle

Storing Data into Variables 3–5A15A12 Result: 15 3 that is,A x TtTtZzZzYyYyX3X3Recall Arithmetic Recall arithmetic uses L,L,Lz, or Lq to do

3–6 Storing Data into Variables Keys: Display: Description: 1ID2IE3IF)))Stores the assumed values into the variable. 1I D I E I

Storing Data into Variables 3–7|Z A )Exchanges contents of the X–register and variable A. |Z A )Exchanges contents of the X–register a

Real–Number Functions 4–14Real–Number Functions This chapter covers most of the calculator's functions that perform computations on real numbers

4–2 Real–Number Functions To Calculate: Press: Natural logarithm (base e)Common logarithm (base 10) {Natural exponential Common exponential (antil

Real–Number Functions 4–3In RPN mode, to calculate a number y raised to a power x, key in yx,then press . (For y > 0, x can be any number; for y

4–4 Real–Number Functions Setting the Angular Mode The angular mode specifies which unit of measure to assume for angles used in trigonometric functio

Real–Number Functions 4–5Example: Show that cosine (5/7)π radians and cosine 128.57° are equal (to four significant digits). Keys: Display: Descri

Contents 5Editing and Clearing Equations ...6–7Types of Equations...

4–6 Real–Number Functions Hyperbolic Functions With x in the display: To Calculate: Press: Hyperbolic sine of x (SINH). {OHyperbolic cosine of x (CO

Real–Number Functions 4–7)Total cost (base price + 6% tax).Suppose that the $15.76 item cost $16.12 last year. What is the percentage change fr

4–8 Real–Number Functions Physics Constants There are 40 physics constants in the CONST menu. You can press |to view the following items. CONST Menu

Real–Number Functions 4–9Items Description Value {TH} Classical electron radius 2.817940285×10–15 m{'µ} Characteristic impendence of vacuum 3

4–10 Real–Number Functions Coordinate Conversions The function names for these conversions are y,xÆθ,r and θ,rÆy,x.Polar coordinates (r,θ) and rectang

Real–Number Functions 4–11Example: Polar to Rectangular Conversion.In the following right triangles, find sides x and y in the triangle on the left,

4–12 Real–Number Functions RCRXc_36.5o77.8 ohmsθKeys: Display: Description:  {}Sets Degrees mode. 36.5^.)Enters θ, degrees of voltage l

Real–Number Functions 4–13|u)Equals 8 minutes and 34.29 seconds.  {%} 4 )Restores FIX 4 display format. Angle Conversions When conve

4–14 Real–Number Functions Probability Functions Factorial To calculate the factorial of a displayed non-negative integer x (0 ≤x≤ 253), press { (the

Real–Number Functions 4–15The RANDOM function uses a seed to generate a random number. Each random number generated becomes the seed for the next ran

6 Contents Using Complex Numbers in Polar Notation... 9–510. Base Conversions and ArithmeticArithmetic in Bases 2, 8, and 16..

4–16 Real–Number Functions Parts of Numbers These functions are primarily used in programming. Integer part To remove the fractional part of x and rep

Real–Number Functions 4–17Names of Functions You might have noticed that the name of a function appears in the display when you press and hold the ke

Fractions 5–15Fractions "Fractions" in chapter 1 introduces the basics about entering, displaying, and calculating with fractions: To ent

5–2 Fractions If you didn't get the same results as the example, you may have accidentally changed how fractions are displayed. (See "Changi

Fractions 5–3Entered Value Internal Value Displayed Fraction 23/8 2.37500000000  +1415/32 14.4687500000  +54/12 4.50000000000  +618/

5–4 Fractions This is especially important if you change the rules about how fractions are displayed. (See "Changing the Fraction Display" l

Fractions 5–5You can select one of three fraction formats. The next few topics show how to change the fraction display. Setting the Maximum Denomin

5–6 Fractions To select a fraction format, you must change the states of two flags. Each flag can be "set" or "clear," and in one

Fractions 5–7Number Entered and Fraction Displayed Fraction Format ¼2 2.5 2 2/3 2.9999 216/25Most precise 2 2 1/2 2 2/3S 3T 2 9/14TFactors of denom

Contents 7Selecting a Mode...12–3Program Boundaries (LBL and RTN) ...12

5–8 Fractions In an equation or program, the RND function does fractional rounding if Fraction–display mode is active. Example: Suppose you have a 56

Fractions 5–9Fractions in Programs When you're typing a program, you can type a number as a fraction — but it's converted to its decimal va

Entering and Evaluating Equations 6–16Entering and Evaluating Equations How You Can Use Equations You can use equations on the HP 33s in several wa

6–2 Entering and Evaluating Equations L¾Begins a new equation, turning on the "¾" equation–entry cursor. L turns on the A..Zannunciator so

Entering and Evaluating Equations 6–3Summary of Equation Operations All equations you create are saved in the equation list. This list is visible w

6–4 Entering and Evaluating Equations Entering Equations into the Equation List The equation list is a collection of equations you enter. The list i

Entering and Evaluating Equations 6–5Numbers in Equations You can enter any valid number in an equation except fractions and numbers that aren&apos

6–6 Entering and Evaluating Equations Parentheses in Equations You can include parentheses in equations to control the order in which operations are

Entering and Evaluating Equations 6–7  ! ! if there are no equations in the equation list or if the equation pointer is at the top of the