How a "REAL NUMBER" is stored in the "float" variable while programming in C ?

Question

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#include<stdio.h>
main()
{
float a,b;
printf("Enter two real number values for a and b :\n");
scanf("%f %f",&a,&b);
printf("a = %f and b = %f\n",a,b);
getch();
}

Input :
456987.2
456987.3
Output :
456987.187500
456987.312500

Why is my output abnormal ? I mean why am i getting only approximate values as output ?

I am using Dev-C++ 5.11 IDE.
My computer has 64-bit architecture.

What I have tried:

I have tried to guess the reason behind the approximation of the real number values to be stored, but i can't come up with an explanation.

Posted 12-Apr-16 5:52am

Shubham_Dubey

Updated 12-Apr-16 22:58pm

v3

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Sergey Alexandrovich Kryukov 12-Apr-16 12:08pm

This is how floating-point numbers work, nothing abnormal. You can format them into string in some more suitable way, if you want.
Do I even need to explain that real numbers can only be represented approximately? (Floating-point numbers are designed to serve as an approximation of the concept of mathematical real numbers.) Do I have to explain why? Do you understand that a real number can contain more information that your whole computer can hold? Do you understand that most real numbers contains infinite volume of information each?
—SA

Shubham_Dubey 12-Apr-16 12:17pm

Sir, would you please send me a link to some related documents/articles so i can read how floating point numbers are stored.

Sergey Alexandrovich Kryukov 12-Apr-16 12:37pm

Oh, sure. Not that you need to directly use it, but it's important to understand, by many reasons.
Please see Solution 4.
—SA

Shubham_Dubey 12-Apr-16 12:44pm

Thanks a lot :)

Sergey Alexandrovich Kryukov 12-Apr-16 12:55pm

You are very welcome.
Good luck, call again.
—SA

4 solutions

Solution 2

This is documented all over the place, thousands of times. What you're looking for is "IEEE floating point number representation[^]".

Posted 12-Apr-16 6:19am

Dave Kreskowiak

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Sergey Alexandrovich Kryukov · Accepted Answer · 2016-04-12T06:26:00

When you declare some variable as float or double, you tell the computer that it's floating-point data, approximate representation of mathematical real numbers. You call them "real" yourself, but then you need to understand the mathematical concept of real numbers. Please see my comment to the question.

They are approximate by definition; and they cannot be precise in principle.

The compile cannot "know" what you may assign to a floating-point value. On next step, you can calculate acos(−1). Even though −1 can be considered as exact value, the result is transcendental number π. Did you ever heard that it can be proven that any given finite sequence of digits can be found in the infinite representation of this number?

Maybe you need fractional but precise number? They are not hard to implement. It could be a record (struct) of two integer numbers: a mantissa and an exponent (say, a power of 10). Roughly, you define an integer number and, separately, the information on where to put a decimal point. And then you can define all operations on these number. Of course, they are nothing like real. You cannot even divide 1 / 3. Or you can, if you make it more advanced: add information on the period, which you can calculate and represent: 1/3 = 0.(3). But if you make this step, you can better implement the concept of rational numbers which is a pair of integers: numerator and denominator.

With floating-points, you also may want to learn numeric data formatting.

—SA

Aescleal · Accepted Answer · 2016-04-12T06:06:00

456987.187500 is the closest number that can be encoded as a single precision floating point number to 456987.2. Changing the least significant bit gives you a value that has a greater difference to 456987.2.

A float on most systems has (from memory) 24 significant bits, which is about 7 or 8 significant decimal digits. As soon as you want to try and represent a number with a greater number of significant bits it'll all go horribly wrong.

If you need more bits of precision try using a double or long double. If that's not enough you might need to look at rolling your own floating point representation or borrowing someone else's.

Sergey Alexandrovich Kryukov · Accepted Answer · 2016-04-12T06:35:00

Shubham_Dubey asked:

Sir, would you please send me a link to some related documents/articles so i can read how floating point numbers are stored.

Oh, sure. This is fully standardized by IEEE 754: IEEE floating point — Wikipedia, the free encyclopedia[^].

See also:
Floating point — Wikipedia, the free encyclopedia[^].

—SA

How a "REAL NUMBER" is stored in the "float" variable while programming in C ?

4 solutions

Solution 2

Solution 3

Solution 1

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