0.1+0.2!=0.3

2019-11-06 06:41:45

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Floating Point MathYour language isn't broken, it's doing floating point math. Computers can only natively store integers, so they need some way of rePResenting decimal numbers. This representation comes with some degree of inaccuracy. That's why, more often than not, .1 + .2 != .3.Why does this happen?It's actually pretty simple. When you have a base 10 system (like ours), it can only express fractions that use a prime factor of the base. The prime factors of 10 are 2 and 5. So 1/2, 1/4, 1/5, 1/8, and 1/10 can all be expressed cleanly because the denominators all use prime factors of 10. In contrast, 1/3, 1/6, and 1/7 are all repeating decimals because their denominators use a prime factor of 3 or 7. In binary (or base 2), the only prime factor is 2. So you can only express fractions cleanly which only contain 2 as a prime factor. In binary, 1/2, 1/4, 1/8 would all be expressed cleanly as decimals. While, 1/5 or 1/10 would be repeating decimals. So 0.1 and 0.2 (1/10 and 1/5) while clean decimals in a base 10 system, are repeating decimals in the base 2 system the computer is Operating in. When you do math on these repeating decimals, you end up with leftovers which carry over when you convert the computer's base 2 (binary) number into a more human readable base 10 number.Below are some examples of sending.1 + .2 to standard output in a variety of languages.

Language	Code	Result
C	#include<stdio.h> int main(int argc, char** argv) { printf("%.17f/n", .1+.2); return 0; }	0.30000000000000004
C++	#include <iomanip> std::cout << setprecision(17) << 0.1 + 0.2 << std.endl;	0.30000000000000004
php	echo .1 + .2;	0.3
PHP converts 0.30000000000000004 to a string and shortens it to "0.3". To achieve the desired floating point result, adjust the precision ini setting: ini_set("precision", 17).
MySQL	SELECT .1 + .2;	0.3
Postgres	SELECT select 0.1::float + 0.2::float;	0.3
Delphi XE5	writeln(0.1 + 0.2);	3.00000000000000E-0001
Erlang	io:format("~w~n", [0.1 + 0.2]).	0.30000000000000004
Elixir	IO.puts(0.1 + 0.2)	0.30000000000000004
Ruby	puts 0.1 + 0.2Andputs 1/10r + 2/10r	0.30000000000000004And3/10
Ruby supports rational numbers in syntax with version 2.1 and newer directly. For older versions use Rational.Ruby also has a library specifically for decimals: BigDecimal.
Python 2	print(.1 + .2)Andfloat(decimal.Decimal(".1") + decimal.Decimal(".2")) And.1 + .2	0.3And0.3And0.30000000000000004
Python 2's "print" statement converts 0.30000000000000004 to a string and shortens it to "0.3". To achieve the desired floating point result, use print(repr(.1 + .2)). This was fixed in Python 3 (see below).
Python 3	print(.1 + .2)And.1 + .2	0.30000000000000004And0.30000000000000004
Lua	print(.1 + .2)print(string.format("%0.17f", 0.1 + 0.2))	0.30.30000000000000004
javaScript	document.writeln(.1 + .2);	0.30000000000000004
Java	System.out.println(.1 + .2);AndSystem.out.println(.1F + .2F);	0.30000000000000004And0.3
Julia	.1 + .2	0.30000000000000004
Julia has built-in rational numbers support and also a built-in arbitrary-precision BigFloat data type. To get the math right, 1//10 + 2//10 returns 3//10.
Clojure	(+ 0.1 0.2)	0.30000000000000004
Clojure supports arbitrary precision and ratios. (+ 0.1M 0.2M) returns 0.3M, while (+ 1/10 2/10) returns 3/10.
C#	Console.WriteLine("{0:R}", .1 + .2);	0.30000000000000004
GHC (Haskell)	0.1 + 0.2	0.30000000000000004
Haskell supports rational numbers. To get the math right, (1 % 10) + (2 % 10) returns 3 % 10.
Hugs (Haskell)	0.1 + 0.2	0.3
bc	0.1 + 0.2	0.3
Nim	echo(0.1 + 0.2)	0.3
Gforth	0.1e 0.2e f+ f.	0.3
dc	0.1 0.2 + p	.3
Racket (PLT Scheme)	(+ .1 .2)And(+ 1/10 2/10)	0.30000000000000004And3/10
Rust	extern crate num; use num::rational::Ratio; fn main() { println!(.1+.2); println!("1/10 + 2/10 = {}", Ratio::new(1, 10) + Ratio::new(2, 10)); }	0.300000000000000043/10
Rust has rational number support from the num crate.
Emacs Lisp	(+ .1 .2)	0.30000000000000004
Turbo Pascal 7.0	writeln(0.1 + 0.2);	3.0000000000E-01
Common Lisp	* (+ .1 .2)And* (+ 1/10 2/10)	0.3And3/10
Go	package main import "fmt" func main() { fmt.Println(.1 + .2) var a float64 = .1 var b float64 = .2 fmt.Println(a + b) fmt.Printf("%.54f/n", .1 + .2) }	0.30.300000000000000040.299999999999999988897769753748434595763683319091796875
Go numeric constants have arbitrary precision.
Objective-C	0.1 + 0.2;	0.300000012
OCaml	0.1 +. 0.2;;	float = 0.300000000000000044
Powershell	PS C:/>0.1 + 0.2	0.3
Prolog (SWI-Prolog)	?- X is 0.1 + 0.2.	X = 0.30000000000000004.
Perl 5	perl -E 'say 0.1+0.2'perl -e 'printf q{%.17f}, 0.1+0.2'	0.30.30000000000000004
Perl 6	perl6 -e 'say 0.1+0.2'perl6 -e 'say sprintf(q{%.17f}, 0.1+0.2)'perl6 -e 'say 1/10+2/10'	0.30.300000000000000000.3
Perl 6, unlike Perl 5, uses rationals by default, so .1 is stored something like { numerator => 1, denominator => 10 }..
R	print(.1+.2)print(.1+.2, digits=18)	0.30.300000000000000044
scala	scala -e 'println(0.1 + 0.2)'Andscala -e 'println(0.1F + 0.2F)' Andscala -e 'println(BigDecimal("0.1") + BigDecimal("0.2"))'	0.30000000000000004And0.3And0.3
Smalltalk	0.1 + 0.2.	0.30000000000000004
Swift	0.1 + 0.2NSString(format: "%.17f", 0.1 + 0.2)	0.30.30000000000000004
D	import std.stdio; void main(string[] args) { writefln("%.17f", .1+.2); writefln("%.17f", .1f+.2f); writefln("%.17f", .1L+.2L); }	0.299999999999999990.300000011920928960.30000000000000000
ABAP	WRITE / CONV f( '.1' + '.2' ).AndWRITE / CONV decfloat16( '.1' + '.2' ).	3.0000000000000004E-01And0.3