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
In reply to @christianp
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?
In reply to @christianp
I've seen gas stations in the US show the tenths part with a fraction instead of a decimal.
Have you seen any other signage with a fixed denominator that isn't 10?
In reply to @christianp
Or, more thrillingly, are there contexts where numbers are written as decimals, but some decimals are illegal?
This is sometimes true for currencies: a price like £1.054 would normally be rounded to the nearest penny. But if it's a price per unit, you might need that extra digit
In reply to @christianp
Percentages highlight an often-ignored point about rounding: if you've got a boundary, rounding to it can be very misleading.
For example, if something works 999 of 1000 times, it's not correct to say it's 100% effective. 99% is further from the true value, but shows the failure.