Let's pretend I have a five places floating-point register.
I have to represent the following numbers: $256.786$ and $256750000$.
I can represent the first number as $2.568 \cdot 10^2$. The relative error would be: $e_r=|\frac{2.568 \cdot 10^2-256.786}{256.786}|=0.00545 \% $
I can represent the second number as $2.568\cdot10^8$ The relative error would be: $e_r=|\frac{2.568 \cdot 10^8-256750000}{256750000}|=0.0194 \% $
I was told in this video that with floating point register, the order of relative error is the same with every number.
But in this case, this isn't true, is it? What's wrong?
Many thanks