# \$fl(x)=x(1+delta)\$

The floating point representation of a real number $$x$$ in a machine is given by $$fl(x)=x(1+delta),: |delta| = frac{|x^*-x|}{|x|} le epsilon$$.

But I do not find this equation very insightful. Insert $$delta = frac{x^*-x}{x}$$ in the equation and you get $$x^*$$. So $$fl(x)$$ is just $$x^*$$. Why write $$x^*$$ in this fancy way: $$fl(x)=x(1+delta)$$

Does equation have a name by the way?