Setting fraction precision

Setting fraction precision

The fraction precision setting determines the precision in which the HP 39G/40G converts a decimal value to a fraction. The greater the precision value that is set, the closer the fraction is to the decimal value.

By choosing a precision of 1 you are saying that the fraction only has to match 0.234 to at least 1 decimal place (3/13 is 0.23076...).

The fractions used are found using the technique of continued fractions.

When converting recurring decimals this can be important. For example, at precision 6 the decimal 0.6666 becomes 3333/5000 (6666/10000) whereas at precision 3, 0.6666 becomes 2/3, which is probably what you would want.

For example, when converting .234 to a fraction, the precision value has the following effect:

•Precision set to 1:

•Precision set to 2:

•Precision set to 3:

•Precision set to 4

Getting started

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Image 35

$HP 40G manual Setting fraction precision$

Contents

USER’S Guide Page Contents Parametric aplet Importing Sample Statistics from the Statistics aplet Inference aplet Variables and memory management Programming Index +,7@CLEAR, 6+,7@MODES, 6+,7@ACOS, etc PrefaceManual conventions @, &26@, +20@, etc Preface Home On/off, cancel operationsGetting started Parts of the display To adjust the contrast To clear the displayDisplay Annunciator Description KeyboardMenu keys Key Meaning Aplet control keys 75@ +,7@$/3+$@ 175@ +,7@$/3+$@ Shifted keystrokesHelpwith Key Description Math keys Program commands Inactive keys To search a menu To cancel a menuMenus Input forms Mode settingsReset input form values Setting Options Setting Options Press+20@ to return to Home Setting a modeAplets E-lessons Aplet Use this aplet to explore Name N T Quad Explorer aplet *,*A, keys Trig Explorer aplet Aplets are stored in the Aplet library Symbolic view Plot view Numeric viewAplet library Aplet views Views menu contains the Plot-Table view To change views Aplet view configurationPlot Setup Numeric Setup Symbolic Configuration Example Mathematical calculationsEntering expressions Long results Negative numbers @4 6+,7@EEX @13@ @@6 6+,7@EEX 23@ j@ 3 6+,7@EEX 175@ Scientific notation powersExplicit and implicit multiplication +,7@√ @85 @9 @ Entering Calculates@ 45 @6+,7@π +,7@√ 85@9 Clearing numbers Using previous results 50175@ @25 175@175@ 175@ updates ANS from 50 to 75 to Key Function Accessing the display history$/3+$@ a 175@ Clearing the display history Using fractionsSetting Fraction mode See Setting fraction precision below for more information Setting fraction precision Evaluate the calculation Fraction calculations Converting decimals to fractionsReturn to Home and enter the calculation @@@2@3 + iy Complex numbersConverting a number to a fraction Complex results To enter complex numbers Storing complex numbers Catalog/Editor ContentsCatalogs and editors Trig Explorer and Quadratic Explorer aplets Differences between the HP 38G and the HP 39G/40GMemory manager Plot Goto function Statistics Pred functionPage Aplet views About the Symbolic viewDefining an expression Symbolic view Aplets and their views Aplets and their views Home Evaluating expressionsAplets +,7@CLEAR Symb view keys$56@ $7+@ 175@ or Setting up the plot Plot view setupPlot view settings About the Plot view Reset plot settings +,7@*A Exploring the graphPlot view keys Zoom options Trace a graphZoom within a graph To jump directly to a value To turn trace on/ off Multiplies vertical scale only, using Divides horizontal scale only, usingMultiplies horizontal scale, using Divides vertical scale only, using =220Zoom Out 018Zoom=220Un-zoom Press *k, to move to the bottom of the Zoom list =220Y-Zoom Out =220X-Zoom=220X-Zoom Out =220Y-Zoom To box zoom To set zoom factors Options Other views for scaling and splitting the graph Menu key copies the right plot to the left Integer scaling Trigonometric scaling About the numeric viewOverlay plots Decimal scaling Reset numeric settings Setting up the table numeric view setupNumeric view settings Zoom within a table Exploring the table of numbersNUM view menu keys 175@, the values for the dependent variables are Building your own table of numbersArrow keys to place the cursor in the independent variable Column, then enter the value to jump to Clear data Build Your Own menu keys +,7@√@9 Example plotting a circle$3/7@ Select Open the Function aplet Function apletAbout the Function aplet Getting started with the Function aplet Plot the functions Define the expressionsPlot the functions @75@175@ Times Change the scale Trace a graphWith FCN functions Trace the linear function Root value is displayed at the bottom of the screen Find the greater of the two roots of the quadratic functionSelectRoot @.2 2Select.SlopeMove the cursor to x = 1 by pressing the *A,or Choose the end value for Display the numeric view Display the numeric view Set up the tableDisplay the numeric setup To find the extremum of the quadratic Move to X = Match the table settings to the pixel columns in the graphExplore the table Display a table of numeric values Area Extremum Isect Root Slope Function aplet interactive analysis Function Description Access FCN variables FCN functions Two selected expressions Symbolic view. DisplaysCursor. You need to have at least $3/ @ Select Plotting a piecewise defined function example=  Page Open the Parametric aplet Define the expressions Parametric apletAbout the Parametric aplet Getting started with the Parametric aplet 360 Set angle measure Set up the plot Plot the expression+,7@PLOT 120 Overlay plot Display the numbersPlot a triangle graph over the existing circle graph +,7@ PlotPage +,7@CLEAR 46+,7@π 2.a Polar apletGetting started with the polar aplet Open the Polar aplet Explore the graph Display the numbers Getting started with the Sequence aplet Sequence aplet starts in the Symbolic viewSequence aplet About the Sequence aplet Keys to assist in the entry of equations Define the expression Select Cobweb Plot Setup, set the Seqplot option to CobwebPlot the sequence Display the table Plot the Fibonacci sequencePage About the Solve aplet Solve aplet Define the equation Define known variables Getting started with the Solve apletOpen the Solve aplet @ Select Auto Solve the unknown variable Plot the equationSolve for the unknown variable a ≈20 times Solve aplet’s NUM view keys Number format Use an initial guess Message Condition Interpreting results Root- Finder at work 180@ 30 175@ 2175@ *e,4175@ *e,*e, to highlight T Plotting to find guessesAt2 x = v0t + $/3+$@X To move cursor to the intersection Plot the graph 3175@*k,*k,*k Using variables in equationsHome variables Initial guess 1400 920 1100 2265 2890 2200 Statistics apletAbout the Statistics aplet Getting started with the Statistics aplet 1400 175@920 175@ 1100 175@2265 175@ 2890 175@2200 175@ Open the Statistics aplet Enter data175@1 175@ 175@5 175@ 175@4 175@ To move to the next column Select2. Linear Choose fit and data columns Explore statistics Setup plotSelect a fit in the Symbolic setup view To move to the FIT1 +2field Display the equation for the best linear fit 6175@ Entering and editing statistical data$7+@ S to highlight To highlight +,7@ FXUVRU Statistics aplet’s NUM view keys 160 175@ 165 175@ 170 175@ 175 175@ 180 175@ $56@ Height cm Frequency Sets will need to be selected againBefore re-use Delete data Angle SettingSave data Select the Sort Order option. You can choose either Defining a regression model 2VARInsert data Sort data values To choose the fit = ax3+bx2+cx+d. Needs at least Fit models To define your own fitFit model Meaning = m lnx + b Statistic Definition Computed statisticsOne-variable Columns for a linear fit only Two-variable You can plot PlottingTo plot statistical data Histogram Box and Whisker Plot Scatter Plot Plot types Coefficient Relative ErrorFitting a curve to0182VAR data Correlation Plotting mark 2VAR Connected points 2VAR Setting up the plot Plot setup view Trouble-shooting a plot Statistics aplet’s Plot view keys Find predicted values Calculating predicted valuesPage Example data Default the input form contains example data. This exampleInference aplet About the Inference aplet Hypothesis Tests Confidence Intervals Getting started with the Inference apletOpen the Inference aplet Inference aplet’s Symb view keys ∝.a∝ Define the inferential method Field name Definition Open the Statistics aplet Open Statistics aplet. Note Reset current settingsImporting Sample Statistics from the Statistics aplet Plot test results @529 175@ @295 175@ @952 175@ @259 175@ @925 175@ @592 175@ Calculate statistics Open Inference aplet 2one.a Choose inference method and typeImport the data Display the confidence interval in the Plot view Display Numeric view Display Plot viewSpecify a 90% confidence interval in the C field E, to move to Field Inputs Hypothesis testsOne-Sample Z-Test Menu name Result Description Two-Sample Z-TestResults One-Proportion Z-Test H0 π1 = π2 Two-Proportion Z-TestSuccesses in the two populations is equal Hypothesis is that the sample mean has some assumed value One-Sample T-TestTest 1 ∝ Selected hypothesis against the null hypothesis. The null Two-Sample T-Test Sample 2 standard deviation Sample 1 standard deviation Confidence level Confidence intervalsConfidence interval calculations that the HP 39G/40G can Perform are based on the Normal Z-distribution or Student’s Deviations, σ1 and σ2, are known Two populations, ∝1 ∝2, when the population standardTwo-Sample Z-Interval Confidence interval for the difference between the means Sample success count One-Proportion Z-Interval Sample 2 success count Two-Proportion Z-IntervalSuccesses in two populations Sample 1 success count One-Sample T-Interval Two-Sample T-Interval Page Math menu Using mathematical functionsMath functions Calculus Loop Stat-Two Complex Matrices To select a functionFunction categories Functions common to keyboard and menus Math functions by categorySyntax Keyboard functions +,7@√ +,7@ASIN+,7@ACOS +,7@ATAN +,7@ n Valuepower+,7@ABS ABSvalue Lower,upper,expression,variable Calculus functionsTaylor Variableexpression Conj Complex number functionsARG Hyperbolic trigonometry Constants EXPM1 List functionsAlog EXP Recurse Loop functionsMatrix functions Iterate Polyform Polynomial functionsPolycoef Polyeval Random Probability functionsComb Perm Utpt UtpcUtpf Utpn Real-number functions Mant HMS→→HMS INT RAD→DEG MODChange Total Xpon Statistics-TwoSign Truncate Quad Symbolic functionsIsolate LINEAR? Quote Trigonometry functions Home Symbolic calculationsSymbolic calculations in the Function aplet Using formal variables Evaluate the function Finding derivativesTo find derivatives GG@$/3+$@S1 GG@@$/3+$@ To find derivatives in the Function aplet’s Symbolic view Thus, substituting X for S1, it can be seen that To find the indefinite integral using formal variables+,7@GG@0 @ $/3+$@ S1 @ 3 @ Show the result format 10-26 Introduction Variables and memory management To store a value Storing and recalling variablesNumeric Precision To store the results of a calculation 65 @$/3+$@A 175@ Vars menuTo use variables Calculations +,7@LIST Names or values of variables into programs List names directly from the keyboard 2contents,.a is copied to the command line$56@ *e,*e,*e,*A $/3+$@L3175@ Category Available names To copy the value of the variable into the edit line To access an aplet variableAplet variables +,7@MEMORY Memory ManagerStart the Memory Manager. a list of variable categories Is displayedPage Matrix Variables MatricesVectors Matrices +,7@*e, or Creating and storing matricesMatrix Catalog keys + 7@CLEAR Select the type of matrix to create To create a matrix in the matrix catalog +,7@*k, *e Working with matricesTo transmit a matrix Clears all elements from the matrix 728 672? 175@ 8 175@ Matrix arithmeticTo multiply and divide by a scalar 175@ 2175@*e 175@ 4175@ $/3+$@M1 j@$/3+$@M2 175@ $/3+$@M1@ $/3+$@M2 175@ +,7@MATRIX Solving systems of linear equations+,7@MATRIX1 175@ 175@7 175@ About functions Matrix functions and commands Argument conventions Inverse EigenvalEigenvv Idenmat Schur RankRownorm Rref Identity Matrix Transposing a Matrix ExamplesTrace TRN Reduced-Row Echelon Form Open the List catalog ListsCreating lists Create a list in the List Catalog List catalog keys List edit keys Create a list @ /@ Displaying and editing listsTo display a list To display one element To edit a list To insert an element in a list To store one element 16a*e To delete all lists Deleting listsTransmitting lists To delete a list List functions $/3+$@A @ $/3+$@L 5175@ $7+@L *A$/3+$@L5175@ $7+@L *A,Select Sorts elements in ascending order Calculates the product of all elements in listPOSlist, element Calculates the number of elements in a list $/3+$@ L1 175@ Finding statistical values for list elements89@65@ 0@89 Go to the Numeric view To display calculated statistics 180@67$76aPage Your work is automatically saved. Press any view key Aplet note viewTo write a note in Note view +,7@letter +,7@ Cmds +,7@%.63$= To draw a line Aplet sketch viewSketch keys Draw keys Where you want any corner of the box to beYou can adjust the size of the box by moving the cursor To draw a box Highlight2. the variable name you want to use and press KeysPress 2.again to affix the label Name of the note is ‘MYNOTE’ To import a graphics variableTo create a note +,7@NOTEPAD Another HP 39G/40G or PC Opens the selected note forBegins a new note, and asks for Transmits the selected note to 14-8 Programming Contents of a Program Structured Programming Open Program catalog Program catalog +,7@*k, or *e Program catalog keys Create a new program Creating and editing programs To enter functions more to come Enter commands Edit a program+,7@CMDS A,*e Editing keys Run a program From HOME, type RUN programname. or Using programsDebug a program Stop a program Transmit a program Delete a program Working with programsCopy a Program Programs Delete the contents of a programAbout customizing an aplet Delete all $3/7@Select Aplet naming conventionCustomizing an aplet example Configuring the Setviews menu option programs Setviews ’’’’’’’’18 Programming 15-13 Select Programming commandsAplet commands Check Syntax for the command is as follows Command syntax Auto-run programs If test-clause Branch commandsUncheck IF...THEN...END END Iferr trap-clause Then error-clause ENDIF... then ELSE... END CASE...END Iferr Then Drawing commands Graphic commands Grobxor →GROBGrobnot Grobor Loop commands Matrix commands Scaleadd RandmatRedim Scale Prompt commands Print commands Editmat matrixname DispDisptime Disp linenumbertextitem Input Input nametitle,labelhelpdefaultGetkey Wait seconds MsgboxPrompt Wait Stat-Two commands Stat-One and Stat-Two commandsStat-One commands Axes Storing and retrieving variables in programsPlot-view variables Area Grid CoordExtremum FastRes Isect HwidthIndep InvCross S1mark-S5mark Nmin / NmaxRecenter Root Umin/Umax SimultSlope StatPlot Xcross Tmin / TmaxTracing Tstep Ymin / Ymax XtickYtick Xmin / Xmax Angle Symbolic-view variablesXzoom Yzoom E1...E9, E0 X1, Y1...X9,Y9 X0,Y0R1...R9, R0 U1...U9, U0 Digits Numeric-view variablesC1...C9, C0 NumIndep FormatNumCol NumFont NumType NumRowNumStart NumStep PageNum Creating new aplets based on existing aplets Extending aplets $/3+$@ C @ 175@ Aplet Keys$/3+$@ H 175@ $1@ $/3+$@ θ @ 180@ 35 175@ $3/ @Select Length of the ladder is approximately 8.72 metres Resetting an apletDownloading e-lessons from the web Solve for the missing To transmit an aplet Sending and receiving aplets To delete an aplet Sorting items in the aplet library menu listTo sort the aplet list Canada Reference informationRegulatory information Warranty LED safety Reference information To reset using the keyboard Resetting the HP 39G/40G 21@ key To erase all memory and reset defaultsIf the calculator does not turn on Cross matrix1,matrix2 Glossary Batteries Operating temperature 0 to 45C 32 to 113FOperating details Category Available name Menu maps of the Vars menuHome variables are Function aplet variables are Function aplet variablesUser-named Modes Parametric aplet variables are Parametric aplet variablesPlot-FCN Polar aplet variables are Polar aplet variables Sequence aplet variables are Sequence aplet variables Solve aplet variables are Solve aplet variables Stat-One Statistics aplet variablesStatistics aplet variables are Calculus Menu maps of the Math menuMath functions Math functions are = = Polynom Program constants Category Command Program commands +,7@ Memory Selected status messagesMessage Meaning Current screen Function value, root, extremumOr intersection is not visible Index Index Index Index Index Index Index Index Index Index Index Index Index