> But that's exploiting the fact that humans treat decimal representations as having implicit denominators That's to say, we know which base we are using... wh

> But that's exploiting the fact that humans treat decimal representations as having implicit denominators That's to say, we know which base we are using... which is a requirement for writing down numbers in the first place. >So say you had a computer that didn't treat base 10 as special Your computer treats base 2 as special. The apples-to-apples comparison would be comparing 355/113 to 11.0010010000111₂ (or a 16-bit float representation of Pi). 355/113 is a better approximation, but not as drastically as you wrote. Writing in binary, 355/113 = 101100011₂/1110001₂, and the equivalent one is 11.0010010000111111011₂ - hardly that big of a difference.