# Problem in comparing Floating point numbers and how to compare them correctly?

In this article, we will see what is the problem in comparing floating-point numbers and we will discuss the correct way to compare two floating-point numbers.

What is the problem in comparing Floating-Point Numbers usually?

Let us first compare two floating-point numbers with the help of relational operator (==).

Example: Using “==” for comparison

## CPP

 `// C++ program to compare ` `// floating point numbers ` ` `  `#include ` `using` `namespace` `std; ` ` `  `void` `compareFloatNum(``double` `a, ``double` `b) ` `{ ` `    ``if` `(a == b) { ` `        ``cout << ``"The numbers are equal"` `             ``<< endl; ` `    ``} ` `    ``else` `{ ` `        ``cout << ``"The numbers are not equal"` `             ``<< endl; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``double` `a = (0.3 * 3) + 0.1; ` `    ``double` `b = 1; ` `    ``compareFloatNum(a, b); ` `} `

## Java

 `// Java program to compare ` `// floating point numbers ` `class` `GFG  ` `{ ` ` `  `    ``static` `void` `compareFloatNum(``double` `a, ``double` `b)  ` `    ``{ ` `        ``if` `(a == b) ` `        ``{ ` `            ``System.out.print(``"The numbers are equal"` `+ ``"\n"``); ` `        ``}  ` `        ``else`  `        ``{ ` `            ``System.out.print(``"The numbers are not equal"` `+ ``"\n"``); ` `        ``} ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``double` `a = (``0.3` `* ``3``) + ``0.1``; ` `        ``double` `b = ``1``; ` `        ``compareFloatNum(a, b); ` `    ``} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

## Python

 `# Python program to compare ` `# floating point numbers ` `def` `compareFloatNum(a, b): ` `    ``if` `(a ``=``=` `b): ` `        ``print``(``"The numbers are equal"``) ` ` `  `    ``else``: ` `        ``print``(``"The numbers are not equal"``) ` ` `  `# Driver code ` ` `  `a ``=` `(``0.3` `*` `3``) ``+` `0.1` `b ``=` `1` `compareFloatNum(a, b) ` ` `  `# This code is contributed by mohit kumar 29 `

## C#

 `// C# program to compare ` `// floating point numbers ` `using` `System; ` ` `  `class` `GFG  ` `{ ` ` `  `    ``static` `void` `comparefloatNum(``double` `a, ``double` `b)  ` `    ``{ ` `        ``if` `(a == b) ` `        ``{ ` `            ``Console.Write(``"The numbers are equal"` `+ ``"\n"``); ` `        ``}  ` `        ``else` `        ``{ ` `            ``Console.Write(``"The numbers are not equal"` `+ ``"\n"``); ` `        ``} ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main(String[] args)  ` `    ``{ ` `        ``double` `a = (0.3 * 3) + 0.1; ` `        ``double` `b = 1; ` `        ``comparefloatNum(a, b); ` `    ``} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

Output:

```The numbers are not equal
```

Why does this problem occur?

In the case of floating-point numbers, the relational operator (==) does not produce correct output, this is due to the internal precision errors in rounding up floating-point numbers.

In the above example, we can see the inaccuracy in comparing two floating-point numbers using “==” operator. The two numbers ‘a’ and ‘b’ are equal ( as (0.3 * 3) + 0.1 = 1 ) but the program results in an incorrect output.

Let’s take a closer look at the numbers in the next snippet.

 `// C++ program to compare ` `// floating point numbers ` ` `  `#include ` `using` `namespace` `std; ` ` `  `void` `printFloatNum(``double` `a, ``double` `b) ` `{ ` `    ``// To print decimal numbers up to 20 digits ` `    ``cout << setprecision(20); ` ` `  `    ``cout << ``"a is : "` `<< a << endl; ` `    ``cout << ``"b is : "` `<< b << endl; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``double` `a = (0.3 * 3) + 0.1; ` `    ``double` `b = 1; ` `    ``printFloatNum(a, b); ` `} `

Output:

```a is : 0.99999999999999988898
b is : 1
```

Now we can see the internal rounding error in floating-point numbers. Number ‘a’ is not correctly rounded up to 1,
there is an internal error in rounding up, a very small error but makes a huge difference when we are comparing the numbers.

How to compare floating-point numbers correctly?
If we do have to compare two floating-point numbers then rather than using “==” operator we will find the absolute difference between the numbers (which if were correctly represented, the difference would have been 0) and compare it with a very small number 1e-9 (i.e 10^-9, this number is very small) and if the difference is less than this number, we can safely say that the two floating-point numbers are equal.

Example:

## C++

 `// C++ program to compare ` `// floating point numbers correctly ` ` `  `#include ` `using` `namespace` `std; ` ` `  `void` `compareFloatNum(``double` `a, ``double` `b) ` `{ ` ` `  `    ``// Correct method to compare ` `    ``// floating-point numbers ` `    ``if` `(``abs``(a - b) < 1e-9) { ` `        ``cout << ``"The numbers are equal "` `             ``<< endl; ` `    ``} ` `    ``else` `{ ` `        ``cout << ``"The numbers are not equal "` `             ``<< endl; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``double` `a = (0.3 * 3) + 0.1; ` `    ``double` `b = 1; ` `    ``compareFloatNum(a, b); ` `} `

## Java

 `// Java program to compare ` `// floating point numbers correctly ` `class` `GFG ` `{ ` ` `  `static` `void` `compareFloatNum(``double` `a, ``double` `b) ` `{ ` ` `  `    ``// Correct method to compare ` `    ``// floating-point numbers ` `    ``if` `(Math.abs(a - b) < 1e-``9``) ` `    ``{ ` `        ``System.out.print(``"The numbers are equal "` `            ``+``"\n"``); ` `    ``} ` `    ``else`  `    ``{ ` `        ``System.out.print(``"The numbers are not equal "` `            ``+``"\n"``); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``double` `a = (``0.3` `* ``3``) + ``0.1``; ` `    ``double` `b = ``1``; ` `    ``compareFloatNum(a, b); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## Python3

 `# Python program to compare ` `# floating ponumbers correctly ` ` `  `def` `compareFloatNum(a, b): ` `     `  `    ``# Correct method to compare ` `    ``# floating-ponumbers ` `    ``if` `(``abs``(a ``-` `b) < ``1e``-``9``): ` `        ``print``(``"The numbers are equal "``); ` `    ``else``: ` `        ``print``(``"The numbers are not equal "``); ` `     `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``a ``=` `(``0.3` `*` `3``) ``+` `0.1``; ` `    ``b ``=` `1``; ` `    ``compareFloatNum(a, b); ` ` `  `# This code is contributed by PrinciRaj1992 `

## C#

 `     `  `// C# program to compare ` `// floating point numbers correctly ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `static` `void` `comparefloatNum(``double` `a, ``double` `b) ` `{ ` ` `  `    ``// Correct method to compare ` `    ``// floating-point numbers ` `    ``if` `(Math.Abs(a - b) < 1e-9) ` `    ``{ ` `        ``Console.Write(``"The numbers are equal "` `            ``+``"\n"``); ` `    ``} ` `    ``else` `    ``{ ` `        ``Console.Write(``"The numbers are not equal "` `            ``+``"\n"``); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``double` `a = (0.3 * 3) + 0.1; ` `    ``double` `b = 1; ` `    ``comparefloatNum(a, b); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```The numbers are equal
```

This code results in the correct output, so whenever two floating point numbers are two be compared then rather than using “==” operator, we will use the above technique.

Attention reader! Don’t stop learning now. Get hold of all the important Java and Collections concepts with the Fundamentals of Java and Java Collections Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.