Why is there an error when adding 0.1 to a number in a loop?

Question

C++ / C#

Here is a C program:
When you enter step dx=0.1 in a loop, an error occurs after the 27th iteration...
What is it from, and how to solve it?

#include <stdio.h>
#include <stdlib.h>

int main(){
    float a, b, c, result, dx, x1, x2, i;

    printf("Enter A\n");
    scanf("%f", &a);

    printf("Enter B\n");
    scanf("%f", &b);

    printf("Enter C\n");
    scanf("%f", &c);

    printf("Enter X1\n");//X1 начальный
    scanf("%f", &x1);

    printf("Enter X2\n");//X2 конечный
    scanf("%f", &x2);

    printf("Enter step - dx\n");
    scanf("%f", &dx);

    printf("\nA = %f\n", a);
    printf("B = %f\n", b);
    printf("C = %f\n", c);
    printf("X1 = %f\n", x1);
    printf("X2 = %f\n\n", x2);
    printf("Step dx = %f\n\n", dx);

    if(x1 < 0 && b != 0){
        printf("X1:\t\tResult:\n\n");
        for(; x1 <= x2; x1+=dx){
            result = a*x1*x1+b;
            printf("%f\t%f\n", x1, result);
        }
    }
    else if(x1 > 0 && b == 0){
        printf("X1:\t\tResult:\n\n");
        for(; x1 <= x2; x1+=dx){
            result = (x1 - a)/(x1 - b);
            printf("%f\t%f\n", x1, result);
        }
    }
    else{
        printf("X1:\t\tResult:\n\n");
        for(; x1 <= x2; x1+=dx){
            result = x1/c;
            printf("%f\t%f\n", x1, result);
        }
    }
    return 0;
}

Answer 1

habrahabr.ru/post/112953

Answer 2

What is it from, and how to solve it?

Nonsense in the question/code is written - unmeasured:
1. "From what" -> Why
2. the for loop is never organized by real types, but should be organized by enumerated types ... mainly int variants
3. your written for loop is poorly written while loop...
4. real values ​​should never be compared for equality ... and certainly should never be a while loop criterion
5. all real operations are approximate , and the condition x1 == x1+ dx, for example, under certain conditions can be true: adding to a number won't change it (think when?)
Sit down - two! ;-)

Answer 3

Because the number 0.1 ₁₀ = 0.0(0011) ₂ is irrational in the binary system, so it has an error in any final representation.

Answer 4

float features. The variable stores a number with an error, this is the data format.