I want as many different conventions for writing numbers as you can give me. I'm interested in contexts where there are different rules for how numbers are written, e.g. scientific notation, percentages, currencies. I'm also interested in 'optional' things like grouping digits.

Which numbers can you represent with different notations? For example, decimals represent numbers of the form a×10ᵇ, so not even all of ℚ! What fruity sets can we find a corresponding notation for?