Retain precision with double in Java

Question

public class doublePrecision       public static void main String   args             double total   0          total    5 6          total    5 8          System out println total             The above code prints   11 399999999999   How would I get this to just print  or be able to use it as  11 4

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Use a BigDecimal  It even lets you specify rounding rules  like ROUND HALF EVEN  which will minimize statistical error by rounding to the even neighbor if both are the same distance  i e  both 1 5 and 2 5 round to 2

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You may want to look into using java s java math BigDecimal class if you really need precision math  Here is a good article from Oracle Sun on the case for BigDecimal  While you can never represent 1 3 as someone mentioned   you can have the power to decide exactly how precise you want the result to be  setScale   is your friend       Ok  because I have way too much time on my hands at the moment here is a code example that relates to your question   import java math BigDecimal         Created by a wonderful programmer known as     Vincent Stoessel    xaymaca gmail com    on Mar 17  2010 at  11 05 16 PM     public class BigUp        public static void main String   args            BigDecimal first  second  result           first   new BigDecimal  33 33333333333333              second   new BigDecimal  100             result   first divide second           System out println  result is     result            will print   result is 0 3333333333333333             and to plug my new favorite language  Groovy  here is a neater example of the same thing   import java math BigDecimal  def  first     new BigDecimal  33 33333333333333   def second   new BigDecimal  100     println  result is     first second      will print  result is 0 33333333333333

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Computers store numbers in binary and can t actually represent numbers such as 33 333333333 or 100 0 exactly   This is one of the tricky things about using doubles   You will have to just round the answer before showing it to a user   Luckily in most applications  you don t need that many decimal places anyhow

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Check out BigDecimal  it handles problems dealing with floating point arithmetic like that   The new call would look like this   term number  coefficient add co     Use setScale   to set the number of decimal place precision to be used

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0 8                     1 2         0 7                     1 3         0 7000000000000002      2 3         0 7999999999999998      4 2                    double adjust   fToInt   1 0 - orgV                      The following two lines works for me           String s   String format  quot   2f quot   adjust           double val   Double parseDouble s            System out println val      output  0 8  0 7  0 7  0 8

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You can t  because 7 3 doesn t have a finite representation in binary   The closest you can get is 2054767329987789 2  48   7 3 1 1407374883553280   Take a look at http   docs python org tutorial floatingpoint html for a further explanation    It s on the Python website  but Java and C   have the same  problem     The solution depends on what exactly your problem is    If it s that you just don t like seeing all those noise digits  then fix your string formatting   Don t display more than 15 significant digits  or 7 for float   If it s that the inexactness of your numbers is breaking things like  if  statements  then you should write if  abs x - 7 3   lt  TOLERANCE  instead of if  x    7 3   If you re working with money  then what you probably really want is decimal fixed point   Store an integer number of cents or whatever the smallest unit of your currency is   VERY UNLIKELY  If you need more than 53 significant bits  15-16 significant digits  of precision  then use a high-precision floating-point type  like BigDecimal

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Observe that you d have the same problem if you used limited-precision decimal arithmetic  and wanted to deal with 1 3  0 333333333   3 is 0 999999999  not 1 00000000    Unfortunately  5 6  5 8 and 11 4 just aren t round numbers in binary  because they involve fifths  So the float representation of them isn t exact  just as 0 3333 isn t exactly 1 3   If all the numbers you use are non-recurring decimals  and you want exact results  use BigDecimal  Or as others have said  if your values are like money in the sense that they re all a multiple of 0 01  or 0 001  or something  then multiply everything by a fixed power of 10 and use int or long  addition and subtraction are trivial  watch out for multiplication    However  if you are happy with binary for the calculation  but you just want to print things out in a slightly friendlier format  try java util Formatter or String format  In the format string specify a precision less than the full precision of a double  To 10 significant figures  say  11 399999999999 is 11 4  so the result will be almost as accurate and more human-readable in cases where the binary result is very close to a value requiring only a few decimal places   The precision to specify depends a bit on how much maths you ve done with your numbers - in general the more you do  the more error will accumulate  but some algorithms accumulate it much faster than others  they re called  unstable  as opposed to  stable  with respect to rounding errors   If all you re doing is adding a few values  then I d guess that dropping just one decimal place of precision will sort things out  Experiment

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If you just want to process values as fractions  you can create a Fraction class which holds a numerator and denominator field   Write methods for add  subtract  multiply and divide as well as a toDouble method  This way you can avoid floats during calculations   EDIT  Quick implementation   public class Fraction    private int numerator  private int denominator   public Fraction int n  int d       numerator   n      denominator   d     public double toDouble        return   double numerator    double denominator       public static Fraction add Fraction a  Fraction b       if a denominator    b denominator           double aTop   b denominator   a numerator          double bTop   a denominator   b numerator          return new Fraction aTop   bTop  a denominator   b denominator             else          return new Fraction a numerator   b numerator  a denominator            public static Fraction divide Fraction a  Fraction b       return new Fraction a numerator   b denominator  a denominator   b numerator      public static Fraction multiply Fraction a  Fraction b       return new Fraction a numerator   b numerator  a denominator   b denominator      public static Fraction subtract Fraction a  Fraction b       if a denominator    b denominator           double aTop   b denominator   a numerator          double bTop   a denominator   b numerator          return new Fraction aTop-bTop  a denominator b denominator             else          return new Fraction a numerator - b numerator  a denominator

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When you input a double number  for example  33 33333333333333  the value you get is actually the closest representable double-precision value  which is exactly   33 3333333333333285963817615993320941925048828125   Dividing that by 100 gives   0 333333333333333285963817615993320941925048828125   which also isn t representable as a double-precision number  so again it is rounded to the nearest representable value  which is exactly   0 3333333333333332593184650249895639717578887939453125   When you print this value out  it gets rounded yet again to 17 decimal digits  giving   0 33333333333333326

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You re running up against the precision limitation of type double   Java Math has some arbitrary-precision arithmetic facilities

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private void getRound            this is very simple and interesting      double a   5  b   3  c      c   a   b      System out println   round  val is     c            round  val is     1 6666666666666667        if you want to only two precision point with double we                  can use formate option in String                which takes 2 parameters one is formte specifier which                shows dicimal places another double value      String s   String format    2f   c       double val   Double parseDouble s       System out println   val is      val          now out put will be   val is  1 67

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Observe that you d have the same problem if you used limited-precision decimal arithmetic  and wanted to deal with 1 3  0 333333333   3 is 0 999999999  not 1 00000000    Unfortunately  5 6  5 8 and 11 4 just aren t round numbers in binary  because they involve fifths  So the float representation of them isn t exact  just as 0 3333 isn t exactly 1 3   If all the numbers you use are non-recurring decimals  and you want exact results  use BigDecimal  Or as others have said  if your values are like money in the sense that they re all a multiple of 0 01  or 0 001  or something  then multiply everything by a fixed power of 10 and use int or long  addition and subtraction are trivial  watch out for multiplication    However  if you are happy with binary for the calculation  but you just want to print things out in a slightly friendlier format  try java util Formatter or String format  In the format string specify a precision less than the full precision of a double  To 10 significant figures  say  11 399999999999 is 11 4  so the result will be almost as accurate and more human-readable in cases where the binary result is very close to a value requiring only a few decimal places   The precision to specify depends a bit on how much maths you ve done with your numbers - in general the more you do  the more error will accumulate  but some algorithms accumulate it much faster than others  they re called  unstable  as opposed to  stable  with respect to rounding errors   If all you re doing is adding a few values  then I d guess that dropping just one decimal place of precision will sort things out  Experiment

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Short answer  Always use BigDecimal and make sure you are using the constructor with  String argument  not the double one   Back to your example  the following code will print 11 4  as you wish   public class doublePrecision       public static void main String   args          BigDecimal total   new BigDecimal  0          total   total add new BigDecimal  5 6           total   total add new BigDecimal  5 8           System out println total

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As others have noted  not all decimal values can be represented as binary since decimal is based on powers of 10 and binary is based on powers of two   If precision matters  use BigDecimal  but if you just want friendly output   System out printf    2f n   total     Will give you   11 40

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Multiply everything by 100 and store it in a long as cents

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Multiply everything by 100 and store it in a long as cents

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Floating point numbers differ from real numbers in that for any given floating point number there is a next higher floating point number  Same as integers  There s no integer between 1 and 2   There s no way to represent 1 3 as a float  There s a float below it and there s a float above it  and there s a certain distance between them  And 1 3 is in that space   Apfloat for Java claims to work with arbitrary precision floating point numbers  but I ve never used it  Probably worth a look  http   www apfloat org apfloat java   A similar question was asked here before Java floating point high precision library

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If you have no choice other than using double values  can use the below code   public static double sumDouble double value1  double value2        double sum   0 0      String value1Str   Double toString value1       int decimalIndex   value1Str indexOf           int value1Precision   0      if  decimalIndex    -1            value1Precision    value1Str length   - 1  - decimalIndex             String value2Str   Double toString value2       decimalIndex   value2Str indexOf           int value2Precision   0      if  decimalIndex    -1            value2Precision    value2Str length   - 1  - decimalIndex             int maxPrecision   value1Precision  gt  value2Precision   value1Precision   value2Precision      sum   value1   value2      String s   String format        maxPrecision    f   sum       sum   Double parseDouble s       return sum

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Multiply everything by 100 and store it in a long as cents

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Use a BigDecimal  It even lets you specify rounding rules  like ROUND HALF EVEN  which will minimize statistical error by rounding to the even neighbor if both are the same distance  i e  both 1 5 and 2 5 round to 2

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Why not use the round   method from Math class      The number of 0s determines how many digits you want after the floating point     here one digit  total    double Math round total   10    10  System out println total      prints 11 4

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Pretty sure you could ve made that into a three line example       If you want exact precision  use BigDecimal   Otherwise  you can use ints multiplied by 10   whatever precision you want

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You re running up against the precision limitation of type double   Java Math has some arbitrary-precision arithmetic facilities

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Use java math BigDecimal  Doubles are binary fractions internally  so they sometimes cannot represent decimal fractions to the exact decimal

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Computers store numbers in binary and can t actually represent numbers such as 33 333333333 or 100 0 exactly   This is one of the tricky things about using doubles   You will have to just round the answer before showing it to a user   Luckily in most applications  you don t need that many decimal places anyhow

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Pretty sure you could ve made that into a three line example       If you want exact precision  use BigDecimal   Otherwise  you can use ints multiplied by 10   whatever precision you want

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Why not use the round   method from Math class      The number of 0s determines how many digits you want after the floating point     here one digit  total    double Math round total   10    10  System out println total      prints 11 4

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Pretty sure you could ve made that into a three line example       If you want exact precision  use BigDecimal   Otherwise  you can use ints multiplied by 10   whatever precision you want

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Short answer  Always use BigDecimal and make sure you are using the constructor with  String argument  not the double one   Back to your example  the following code will print 11 4  as you wish   public class doublePrecision       public static void main String   args          BigDecimal total   new BigDecimal  0          total   total add new BigDecimal  5 6           total   total add new BigDecimal  5 8           System out println total

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When you input a double number  for example  33 33333333333333  the value you get is actually the closest representable double-precision value  which is exactly   33 3333333333333285963817615993320941925048828125   Dividing that by 100 gives   0 333333333333333285963817615993320941925048828125   which also isn t representable as a double-precision number  so again it is rounded to the nearest representable value  which is exactly   0 3333333333333332593184650249895639717578887939453125   When you print this value out  it gets rounded yet again to 17 decimal digits  giving   0 33333333333333326

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Observe that you d have the same problem if you used limited-precision decimal arithmetic  and wanted to deal with 1 3  0 333333333   3 is 0 999999999  not 1 00000000    Unfortunately  5 6  5 8 and 11 4 just aren t round numbers in binary  because they involve fifths  So the float representation of them isn t exact  just as 0 3333 isn t exactly 1 3   If all the numbers you use are non-recurring decimals  and you want exact results  use BigDecimal  Or as others have said  if your values are like money in the sense that they re all a multiple of 0 01  or 0 001  or something  then multiply everything by a fixed power of 10 and use int or long  addition and subtraction are trivial  watch out for multiplication    However  if you are happy with binary for the calculation  but you just want to print things out in a slightly friendlier format  try java util Formatter or String format  In the format string specify a precision less than the full precision of a double  To 10 significant figures  say  11 399999999999 is 11 4  so the result will be almost as accurate and more human-readable in cases where the binary result is very close to a value requiring only a few decimal places   The precision to specify depends a bit on how much maths you ve done with your numbers - in general the more you do  the more error will accumulate  but some algorithms accumulate it much faster than others  they re called  unstable  as opposed to  stable  with respect to rounding errors   If all you re doing is adding a few values  then I d guess that dropping just one decimal place of precision will sort things out  Experiment

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Doubles are approximations of the decimal numbers in your Java source   You re seeing the consequence of the mismatch between the double  which is a binary-coded value  and your source  which is decimal-coded    Java s producing the closest binary approximation   You can use the java text DecimalFormat to display a better-looking decimal value

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Do not waste your efford using BigDecimal  In 99 99999  cases you don t need it  java double type is of cource approximate but in almost all cases  it is sufficiently precise  Mind that your have an error at 14th significant digit  This is really negligible   To get nice output use   System out printf    2f n   total

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Do not waste your efford using BigDecimal  In 99 99999  cases you don t need it  java double type is of cource approximate but in almost all cases  it is sufficiently precise  Mind that your have an error at 14th significant digit  This is really negligible   To get nice output use   System out printf    2f n   total

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You may want to look into using java s java math BigDecimal class if you really need precision math  Here is a good article from Oracle Sun on the case for BigDecimal  While you can never represent 1 3 as someone mentioned   you can have the power to decide exactly how precise you want the result to be  setScale   is your friend       Ok  because I have way too much time on my hands at the moment here is a code example that relates to your question   import java math BigDecimal         Created by a wonderful programmer known as     Vincent Stoessel    xaymaca gmail com    on Mar 17  2010 at  11 05 16 PM     public class BigUp        public static void main String   args            BigDecimal first  second  result           first   new BigDecimal  33 33333333333333              second   new BigDecimal  100             result   first divide second           System out println  result is     result            will print   result is 0 3333333333333333             and to plug my new favorite language  Groovy  here is a neater example of the same thing   import java math BigDecimal  def  first     new BigDecimal  33 33333333333333   def second   new BigDecimal  100     println  result is     first second      will print  result is 0 33333333333333

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You can t  because 7 3 doesn t have a finite representation in binary   The closest you can get is 2054767329987789 2  48   7 3 1 1407374883553280   Take a look at http   docs python org tutorial floatingpoint html for a further explanation    It s on the Python website  but Java and C   have the same  problem     The solution depends on what exactly your problem is    If it s that you just don t like seeing all those noise digits  then fix your string formatting   Don t display more than 15 significant digits  or 7 for float   If it s that the inexactness of your numbers is breaking things like  if  statements  then you should write if  abs x - 7 3   lt  TOLERANCE  instead of if  x    7 3   If you re working with money  then what you probably really want is decimal fixed point   Store an integer number of cents or whatever the smallest unit of your currency is   VERY UNLIKELY  If you need more than 53 significant bits  15-16 significant digits  of precision  then use a high-precision floating-point type  like BigDecimal

User · Answer

Pretty sure you could ve made that into a three line example       If you want exact precision  use BigDecimal   Otherwise  you can use ints multiplied by 10   whatever precision you want

User · Answer

Observe that you d have the same problem if you used limited-precision decimal arithmetic  and wanted to deal with 1 3  0 333333333   3 is 0 999999999  not 1 00000000    Unfortunately  5 6  5 8 and 11 4 just aren t round numbers in binary  because they involve fifths  So the float representation of them isn t exact  just as 0 3333 isn t exactly 1 3   If all the numbers you use are non-recurring decimals  and you want exact results  use BigDecimal  Or as others have said  if your values are like money in the sense that they re all a multiple of 0 01  or 0 001  or something  then multiply everything by a fixed power of 10 and use int or long  addition and subtraction are trivial  watch out for multiplication    However  if you are happy with binary for the calculation  but you just want to print things out in a slightly friendlier format  try java util Formatter or String format  In the format string specify a precision less than the full precision of a double  To 10 significant figures  say  11 399999999999 is 11 4  so the result will be almost as accurate and more human-readable in cases where the binary result is very close to a value requiring only a few decimal places   The precision to specify depends a bit on how much maths you ve done with your numbers - in general the more you do  the more error will accumulate  but some algorithms accumulate it much faster than others  they re called  unstable  as opposed to  stable  with respect to rounding errors   If all you re doing is adding a few values  then I d guess that dropping just one decimal place of precision will sort things out  Experiment

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Multiply everything by 100 and store it in a long as cents

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private void getRound            this is very simple and interesting      double a   5  b   3  c      c   a   b      System out println   round  val is     c            round  val is     1 6666666666666667        if you want to only two precision point with double we                  can use formate option in String                which takes 2 parameters one is formte specifier which                shows dicimal places another double value      String s   String format    2f   c       double val   Double parseDouble s       System out println   val is      val          now out put will be   val is  1 67

User · Answer

As others have noted  not all decimal values can be represented as binary since decimal is based on powers of 10 and binary is based on powers of two   If precision matters  use BigDecimal  but if you just want friendly output   System out printf    2f n   total     Will give you   11 40

User · Answer

Doubles are approximations of the decimal numbers in your Java source   You re seeing the consequence of the mismatch between the double  which is a binary-coded value  and your source  which is decimal-coded    Java s producing the closest binary approximation   You can use the java text DecimalFormat to display a better-looking decimal value

User · Answer

Use a BigDecimal  It even lets you specify rounding rules  like ROUND HALF EVEN  which will minimize statistical error by rounding to the even neighbor if both are the same distance  i e  both 1 5 and 2 5 round to 2

User · Answer

Doubles are approximations of the decimal numbers in your Java source   You re seeing the consequence of the mismatch between the double  which is a binary-coded value  and your source  which is decimal-coded    Java s producing the closest binary approximation   You can use the java text DecimalFormat to display a better-looking decimal value

User · Answer

If you have no choice other than using double values  can use the below code   public static double sumDouble double value1  double value2        double sum   0 0      String value1Str   Double toString value1       int decimalIndex   value1Str indexOf           int value1Precision   0      if  decimalIndex    -1            value1Precision    value1Str length   - 1  - decimalIndex             String value2Str   Double toString value2       decimalIndex   value2Str indexOf           int value2Precision   0      if  decimalIndex    -1            value2Precision    value2Str length   - 1  - decimalIndex             int maxPrecision   value1Precision  gt  value2Precision   value1Precision   value2Precision      sum   value1   value2      String s   String format        maxPrecision    f   sum       sum   Double parseDouble s       return sum

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Use java math BigDecimal  Doubles are binary fractions internally  so they sometimes cannot represent decimal fractions to the exact decimal

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As others have mentioned  you ll probably want to use the BigDecimal class  if you want to have an exact representation of 11 4   Now  a little explanation into why this is happening   The float and double primitive types in Java are floating point numbers  where the number is stored as a binary representation of a fraction and a exponent   More specifically  a double-precision floating point value such as the double type is a 64-bit value  where    1 bit denotes the sign  positive or negative   11 bits for the exponent  52 bits for the significant digits  the fractional part as a binary     These parts are combined to produce a double representation of a value    Source  Wikipedia  Double precision   For a detailed description of how floating point values are handled in Java  see the Section 4 2 3  Floating-Point Types  Formats  and Values of the Java Language Specification   The byte  char  int  long types are fixed-point numbers  which are exact representions of numbers  Unlike fixed point numbers  floating point numbers will some times  safe to assume  most of the time   not be able to return an exact representation of a number  This is the reason why you end up with 11 399999999999 as the result of 5 6   5 8   When requiring a value that is exact  such as 1 5 or 150 1005  you ll want to use one of the fixed-point types  which will be able to represent the number exactly   As has been mentioned several times already  Java has a BigDecimal class which will handle very large numbers and very small numbers    From the Java API Reference for the BigDecimal class      Immutable    arbitrary-precision signed decimal   numbers  A BigDecimal consists of an   arbitrary precision integer unscaled   value and a 32-bit integer scale  If   zero or positive  the scale is the   number of digits to the right of the   decimal point  If negative  the   unscaled value of the number is   multiplied by ten to the power of the   negation of the scale  The value of   the number represented by the   BigDecimal is therefore  unscaledValue      10 -scale     There has been many questions on Stack Overflow relating to the matter of floating point numbers and its precision  Here is a list of related questions that may be of interest    Why do I see a double variable initialized to some value like 21 4 as 21 399999618530273  How to print really big numbers in C   How is floating point stored  When does it matter  Use Float or Decimal for Accounting Application Dollar Amount    If you really want to get down to the nitty gritty details of floating point numbers  take a look at What Every Computer Scientist Should Know About Floating-Point Arithmetic

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If you just want to process values as fractions  you can create a Fraction class which holds a numerator and denominator field   Write methods for add  subtract  multiply and divide as well as a toDouble method  This way you can avoid floats during calculations   EDIT  Quick implementation   public class Fraction    private int numerator  private int denominator   public Fraction int n  int d       numerator   n      denominator   d     public double toDouble        return   double numerator    double denominator       public static Fraction add Fraction a  Fraction b       if a denominator    b denominator           double aTop   b denominator   a numerator          double bTop   a denominator   b numerator          return new Fraction aTop   bTop  a denominator   b denominator             else          return new Fraction a numerator   b numerator  a denominator            public static Fraction divide Fraction a  Fraction b       return new Fraction a numerator   b denominator  a denominator   b numerator      public static Fraction multiply Fraction a  Fraction b       return new Fraction a numerator   b numerator  a denominator   b denominator      public static Fraction subtract Fraction a  Fraction b       if a denominator    b denominator           double aTop   b denominator   a numerator          double bTop   a denominator   b numerator          return new Fraction aTop-bTop  a denominator b denominator             else          return new Fraction a numerator - b numerator  a denominator

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As others have mentioned  you ll probably want to use the BigDecimal class  if you want to have an exact representation of 11 4   Now  a little explanation into why this is happening   The float and double primitive types in Java are floating point numbers  where the number is stored as a binary representation of a fraction and a exponent   More specifically  a double-precision floating point value such as the double type is a 64-bit value  where    1 bit denotes the sign  positive or negative   11 bits for the exponent  52 bits for the significant digits  the fractional part as a binary     These parts are combined to produce a double representation of a value    Source  Wikipedia  Double precision   For a detailed description of how floating point values are handled in Java  see the Section 4 2 3  Floating-Point Types  Formats  and Values of the Java Language Specification   The byte  char  int  long types are fixed-point numbers  which are exact representions of numbers  Unlike fixed point numbers  floating point numbers will some times  safe to assume  most of the time   not be able to return an exact representation of a number  This is the reason why you end up with 11 399999999999 as the result of 5 6   5 8   When requiring a value that is exact  such as 1 5 or 150 1005  you ll want to use one of the fixed-point types  which will be able to represent the number exactly   As has been mentioned several times already  Java has a BigDecimal class which will handle very large numbers and very small numbers    From the Java API Reference for the BigDecimal class      Immutable    arbitrary-precision signed decimal   numbers  A BigDecimal consists of an   arbitrary precision integer unscaled   value and a 32-bit integer scale  If   zero or positive  the scale is the   number of digits to the right of the   decimal point  If negative  the   unscaled value of the number is   multiplied by ten to the power of the   negation of the scale  The value of   the number represented by the   BigDecimal is therefore  unscaledValue      10 -scale     There has been many questions on Stack Overflow relating to the matter of floating point numbers and its precision  Here is a list of related questions that may be of interest    Why do I see a double variable initialized to some value like 21 4 as 21 399999618530273  How to print really big numbers in C   How is floating point stored  When does it matter  Use Float or Decimal for Accounting Application Dollar Amount    If you really want to get down to the nitty gritty details of floating point numbers  take a look at What Every Computer Scientist Should Know About Floating-Point Arithmetic

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Floating point numbers differ from real numbers in that for any given floating point number there is a next higher floating point number  Same as integers  There s no integer between 1 and 2   There s no way to represent 1 3 as a float  There s a float below it and there s a float above it  and there s a certain distance between them  And 1 3 is in that space   Apfloat for Java claims to work with arbitrary precision floating point numbers  but I ve never used it  Probably worth a look  http   www apfloat org apfloat java   A similar question was asked here before Java floating point high precision library

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Check out BigDecimal  it handles problems dealing with floating point arithmetic like that   The new call would look like this   term number  coefficient add co     Use setScale   to set the number of decimal place precision to be used

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As others have noted  not all decimal values can be represented as binary since decimal is based on powers of 10 and binary is based on powers of two   If precision matters  use BigDecimal  but if you just want friendly output   System out printf    2f n   total     Will give you   11 40

User · Answer

As others have mentioned  you ll probably want to use the BigDecimal class  if you want to have an exact representation of 11 4   Now  a little explanation into why this is happening   The float and double primitive types in Java are floating point numbers  where the number is stored as a binary representation of a fraction and a exponent   More specifically  a double-precision floating point value such as the double type is a 64-bit value  where    1 bit denotes the sign  positive or negative   11 bits for the exponent  52 bits for the significant digits  the fractional part as a binary     These parts are combined to produce a double representation of a value    Source  Wikipedia  Double precision   For a detailed description of how floating point values are handled in Java  see the Section 4 2 3  Floating-Point Types  Formats  and Values of the Java Language Specification   The byte  char  int  long types are fixed-point numbers  which are exact representions of numbers  Unlike fixed point numbers  floating point numbers will some times  safe to assume  most of the time   not be able to return an exact representation of a number  This is the reason why you end up with 11 399999999999 as the result of 5 6   5 8   When requiring a value that is exact  such as 1 5 or 150 1005  you ll want to use one of the fixed-point types  which will be able to represent the number exactly   As has been mentioned several times already  Java has a BigDecimal class which will handle very large numbers and very small numbers    From the Java API Reference for the BigDecimal class      Immutable    arbitrary-precision signed decimal   numbers  A BigDecimal consists of an   arbitrary precision integer unscaled   value and a 32-bit integer scale  If   zero or positive  the scale is the   number of digits to the right of the   decimal point  If negative  the   unscaled value of the number is   multiplied by ten to the power of the   negation of the scale  The value of   the number represented by the   BigDecimal is therefore  unscaledValue      10 -scale     There has been many questions on Stack Overflow relating to the matter of floating point numbers and its precision  Here is a list of related questions that may be of interest    Why do I see a double variable initialized to some value like 21 4 as 21 399999618530273  How to print really big numbers in C   How is floating point stored  When does it matter  Use Float or Decimal for Accounting Application Dollar Amount    If you really want to get down to the nitty gritty details of floating point numbers  take a look at What Every Computer Scientist Should Know About Floating-Point Arithmetic

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Use a BigDecimal  It even lets you specify rounding rules  like ROUND HALF EVEN  which will minimize statistical error by rounding to the even neighbor if both are the same distance  i e  both 1 5 and 2 5 round to 2

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As others have mentioned  you ll probably want to use the BigDecimal class  if you want to have an exact representation of 11 4   Now  a little explanation into why this is happening   The float and double primitive types in Java are floating point numbers  where the number is stored as a binary representation of a fraction and a exponent   More specifically  a double-precision floating point value such as the double type is a 64-bit value  where    1 bit denotes the sign  positive or negative   11 bits for the exponent  52 bits for the significant digits  the fractional part as a binary     These parts are combined to produce a double representation of a value    Source  Wikipedia  Double precision   For a detailed description of how floating point values are handled in Java  see the Section 4 2 3  Floating-Point Types  Formats  and Values of the Java Language Specification   The byte  char  int  long types are fixed-point numbers  which are exact representions of numbers  Unlike fixed point numbers  floating point numbers will some times  safe to assume  most of the time   not be able to return an exact representation of a number  This is the reason why you end up with 11 399999999999 as the result of 5 6   5 8   When requiring a value that is exact  such as 1 5 or 150 1005  you ll want to use one of the fixed-point types  which will be able to represent the number exactly   As has been mentioned several times already  Java has a BigDecimal class which will handle very large numbers and very small numbers    From the Java API Reference for the BigDecimal class      Immutable    arbitrary-precision signed decimal   numbers  A BigDecimal consists of an   arbitrary precision integer unscaled   value and a 32-bit integer scale  If   zero or positive  the scale is the   number of digits to the right of the   decimal point  If negative  the   unscaled value of the number is   multiplied by ten to the power of the   negation of the scale  The value of   the number represented by the   BigDecimal is therefore  unscaledValue      10 -scale     There has been many questions on Stack Overflow relating to the matter of floating point numbers and its precision  Here is a list of related questions that may be of interest    Why do I see a double variable initialized to some value like 21 4 as 21 399999618530273  How to print really big numbers in C   How is floating point stored  When does it matter  Use Float or Decimal for Accounting Application Dollar Amount    If you really want to get down to the nitty gritty details of floating point numbers  take a look at What Every Computer Scientist Should Know About Floating-Point Arithmetic

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Doubles are approximations of the decimal numbers in your Java source   You re seeing the consequence of the mismatch between the double  which is a binary-coded value  and your source  which is decimal-coded    Java s producing the closest binary approximation   You can use the java text DecimalFormat to display a better-looking decimal value

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0 8                     1 2         0 7                     1 3         0 7000000000000002      2 3         0 7999999999999998      4 2                    double adjust   fToInt   1 0 - orgV                      The following two lines works for me           String s   String format  quot   2f quot   adjust           double val   Double parseDouble s            System out println val      output  0 8  0 7  0 7  0 8

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As others have noted  not all decimal values can be represented as binary since decimal is based on powers of 10 and binary is based on powers of two   If precision matters  use BigDecimal  but if you just want friendly output   System out printf    2f n   total     Will give you   11 40

[java] Retain precision with double in Java

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