Compound condition in C: if (0.0 < a < 1.0)

Because of left-to-right associativity of < operator the expression condition (0.0 < a < 1.0) means ((0.0 < a) < 1.0) == 1 < 1.0 or 0 < 1.0 depending on value of a.

So no, its not identical to if (0.0 < a && a < 1.0) (perhaps you might confusing from Python compassion rule) but in C it will be interpenetrated as I explained above.

A difference you can observe in an example — 0.0 < a < 1.0 == true when a == 0.0, where as (0.0 < a && a < 1.0) == false, for a == 0.0, below is my code (read comments):

#include<stdio.h>
void print_(int c){
    c ? printf("True \n"):
        printf("False \n");
}
int main(void){
    float a = 0.0f;
    print_(0.0f < a < 1.0f); // 0.0 < 0.0 < 1.0f == 0 < 1.0f == True
    print_(0.0f < a && a < 1.0f); // 0.0f < 0.0f && ... ==  False && ... = False
    return 0;
}

output:

True 
False

Check its working @Ideone