That's one of the (many) problems with ieee floats: they "waste" as much bits for mantissa precision in the range of 10^0, 10^1, 10^2, etc, as they do in 10^300 or 10^-300!
Proposals like Posits aim to improve on this :)
Proposals like Posits aim to improve on this :)
A great thing in the Posit proposal is that they also consider a distinct accumulator type for things like sums and dot product. In my experience (I did a PhD on measuring floating point error in large numerical simulations) those operations are the ones that are most likely to sneak on you and need fixing. But most people don't realize that those accumulator type are actually easy to use with IEEE floats, they are entirely orthogonal to using Posits.