C program float f = 123.456;why f in memory is "123.456001"

Question

C program float f = 123.456;why f in memory is "123.456001".

#include<stdio.h>
main()
{
    float f = 123.456;
    printf("%f**%10.2f**%.3f\n", f, f, f);
    printf("%f**%e**%g**\n", f, f, f);
}

123.456001

why 0.000001 ?

It's not even 123.456001, but there are more decimals to come after the '1'. — Aki Suihkonen, May 28 '13 at 14:01
[What Every Computer Scientist Should Know About Floating-Point Arithmetic](http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html) — glglgl, May 28 '13 at 14:02

Johan Råde · Accepted Answer · 2013-05-29T15:24:01.847

4

The binary expansion of

123.456

is

1111011.0111010010111100011010100111111011111001110111...

The computer rounds this off to

1111011.01110100101111001

This is the number that is actually stored in the memory.

The decimal expansion of this number is

123.45600128173828125...

which was printed rounded off to

123.456001

edited May 29 '13 at 15:24

answered May 28 '13 at 14:07

Johan Råde

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I know it, but I can't understand. I know A\D or D\A; i can't understand why is 0.000001 in C program. – kangear May 28 '13 at 14:19
@kangear: See my revised answer. – Johan Råde May 28 '13 at 17:33
Thks very much! I understand. – kangear Jun 05 '13 at 12:44

score 1 · Answer 2 · answered May 28 '13 at 14:01

1

Not every number can be represented exactly by a computer, that would require infinite memory. So floating point number are rounded to the nearest representable number.

answered May 28 '13 at 14:01

Noctua

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C program float f = 123.456;why f in memory is "123.456001"

2 Answers2