Yes, it would be infinitely long (equal to 0.333...)
Whether a metre long segment can be split into three equal parts is probably not something that this sort of maths can sort out. Firstly, although we are splitting 1 segment, that 1 segment is made up of trillions upon trillions of atoms. If those atoms were arranged in a perfect order, and were of an amount divisible by three, then you could theoretically split the segment into three (each piece having the same amount of atoms).
Of course, practically this is probably impossible to do. In mathematics, this is just another quirk of number theory, not really applicable to the real world (since in the real world, infinity may not even exist).
Whether a metre long segment can be split into three equal parts is probably not something that this sort of maths can sort out. Firstly, although we are splitting 1 segment, that 1 segment is made up of trillions upon trillions of atoms. If those atoms were arranged in a perfect order, and were of an amount divisible by three, then you could theoretically split the segment into three (each piece having the same amount of atoms).
Of course, practically this is probably impossible to do. In mathematics, this is just another quirk of number theory, not really applicable to the real world (since in the real world, infinity may not even exist).
