2.7.5 Output Formats for Numbers

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2.7 Textual Output 409option namedefault valueDigitBlock Infinity maximum length of blocks of digits between breaksNumberSeparator {",", " "} strings to insert at breaks between blocks of digits totheleftandrightofadecimalpointNumberPoint "." string to use for a decimal pointNumberSigns {"-", ""} strings to use for signs of negative and positivenumbersNumberPadding {"", ""} strings to use for padding on the left and rightSignPadding False whether to insert padding after the signNumberFormat Automatic function to generate final format of numberExponentFunction Automatic function to determine the exponent to useOptions for number formatting.All the options in the table except the last one apply to both integers and approximate real numbers.All the options can be used in any of the functions NumberForm, ScientificForm, EngineeringFormand AccountingForm. In fact, you can in principle reproduce the behavior of any one of these functionssimply by giving appropriate options settings in one of the others. The default option settingslisted in the table are those for NumberForm.Setting DigitBlock->n breaks digitsinto blocks of length n.You can specify any string to use as aseparator between blocks of digits.This gives an explicit plus sign forpositive numbers, and uses | in place ofa decimal point.In[8]:= NumberForm[30!, DigitBlock->3]Out[8]//NumberForm= 265,252,859,812,191,058,636,308,480,000,000In[9]:= NumberForm[30!, DigitBlock->5, NumberSeparator->" "]Out[9]//NumberForm= 265 25285 98121 91058 63630 84800 00000In[10]:= NumberForm[{4.5, -6.8}, NumberSigns->{"-", "+"},NumberPoint->"|"]Out[10]//NumberForm= {+4|5, -6|8}When Mathematica prints an approximate real number, it has to choose whether scientific notationshould be used, and if so, how many digits should appear to the left of the decimal point. What Mathematicadoes is first to find out what the exponent would be if scientific notation were used, and onedigit were given to the left of the decimal point. Then it takes this exponent, and applies any functiongiven as the setting for the option ExponentFunction. This function should return the actual exponentto be used, or Null if scientific notation should not be used.The default is to use scientific notationfor all numbers with exponents outsidethe range -5 to 5.In[11]:= {8.^5, 11.^7, 13.^9}7 10Out[11]= {32768., 1.94872 10 , 1.06045 10 }Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcoverISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: info@wolfram.com;http://www.wolfram.com/; 1-800-441-6284.© 1991 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction,or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited.
410 2. Principles of MathematicaThis uses scientific notation only fornumbers with exponents of 10 or more.This forces all exponents to be multiplesof 3.In[12]:= NumberForm[%,ExponentFunction -> (If[-10 < # < 10, Null, #]&)]10Out[12]//NumberForm= {32768., 19487171., 1.06045 10 }In[13]:= NumberForm[%, ExponentFunction -> (3 Quotient[#, 3]&)]3 6 9Out[13]//NumberForm= {32.768 10 , 19.4872 10 , 10.6045 10 }Having determined what the mantissa and exponent for a number should be, the final step is to assemblethese into the object to print. The option NumberFormat allows you to give an arbitrary functionwhich specifies the print form for the number. The function takes as arguments three strings: themantissa, the base, and the exponent for the number. If there is no exponent, it is given as "".This gives the exponents in Fortran-like“e” format.You can use FortranForm to printindividual numbers in Fortran format.In[14]:= NumberForm[{5.6^10, 7.8^20},NumberFormat -> (SequenceForm[#1, "e", #3]&) ]Out[14]//NumberForm= {3.03305e7, 6.94852e17}In[15]:= FortranForm[7.8^20]Out[15]//FortranForm= 6.94852e17PaddedForm[expr, tot]PaddedForm[expr, {tot, frac}]NumberForm[expr, {tot, frac}]ColumnForm[{expr 1, expr 2, ... }]print with all numbers having room for tot digits, paddingwith leading spaces if necessaryprint with all numbers having room for tot digits, withexactly frac digits to the right of the decimal pointprint with all numbers having at most tot digits, exactly fracof them to the right of the decimal pointprint with the expr iin a columnControlling the alignment of numbers in output.Whenever you print a collection of numbers in a column or some other definite arrangement, youtypically need to be able to align the numbers in a definite way. Usually you want all the numbers tobe set up so that the digit corresponding to a particular power of 10 always appears at the same positionwithin the region used to print a number.You can change the positions of digits in the printed form of a number by “padding” it in variousways. You can pad on the right, typically adding zeros somewhere after the decimal. Or you can padon the left, typically inserting spaces, in place of leading zeros.This pads with spaces to make room forup to 7 digits in each integer.In[16]:= PaddedForm[{456, 12345, 12}, 7]Out[16]//PaddedForm= { 456, 12345, 12}Web sample page from The Mathematica Book, Second Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcoverISBN 0-201-51502-4; softcover ISBN 0-201-51507-5). To order Mathematica or this book contact Wolfram Research: info@wolfram.com;http://www.wolfram.com/; 1-800-441-6284.© 1991 Wolfram Research, Inc. Permission is hereby granted for web users to make one paper copy of this page for their personal use. Further reproduction,or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited.
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2.7.5 Output Formats for Numbers

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