为什么浮点数乘以时没有错误？(Why there is no errors while multiplying floating point numbers?)

 我需要对浮点数学进行一些澄清。 
 
 我为学习者写了一些代码： 
 
#include "stdio.h"

int main (int argc, char const *argv[])
{
    int i;
    double a=1.0/10.0;
    double sum=0;

    for(i = 0; i < 10; ++i)
        sum+=a;

    printf("%.17G\n", 10*a );
    printf("%d\n", (10*a == 1.0) );

    printf("%.17G\n", sum );
    printf("%d\n", (sum == 1.0) );

    return 0;
}
 
 它给出的输出是： 
 
    1
    1
    0.99999999999999989
    0
 
 为什么（sum == 1.0） - 是假的是相当可理解的，但为什么乘法给出正确答案而没有错误？ 
 
 谢谢。 

I need some clearification about floating point math.
 
I have wrote some code for the learning purpouses:
 
#include "stdio.h"

int main (int argc, char const *argv[])
{
    int i;
    double a=1.0/10.0;
    double sum=0;

    for(i = 0; i < 10; ++i)
        sum+=a;

    printf("%.17G\n", 10*a );
    printf("%d\n", (10*a == 1.0) );

    printf("%.17G\n", sum );
    printf("%d\n", (sum == 1.0) );

    return 0;
}
 
and the output it gives is:
 
    1
    1
    0.99999999999999989
    0
 
Why (sum == 1.0) - is false is pretty understandabale, but why multiplying gives the right answer without the error?
 
Thanks.

原文：https://stackoverflow.com/questions/21654098