Languishing in an exceedingly boring meeting a few weeks ago, making no effort to look engaged, I started playing around with fractions. My discovery (banal, though it was) excited me.

One can use hexadecimal numbers while doing elementary school style fractions and everything works just as one would expect with base-10.

For example (from my scribblings): 


  F0  ?  F

  --  = --

 100    10



 ---> 240  ?  15

      ---  =  --

      256     16

It all holds. Of course, when I was reducing by 0x10 with the hex fractions I was really dividing both sides by 16. This lead me to wonder what would happen with decimals. Can I sensibly talk about $1.FF? It seems like I should be able to, though CALC.EXE only lets me do integer division in HEX mode. Each place to the right of the decimal is a negative power of 16, in exactly the same way that each place to the left of the decimal is a positive power of 16. This must be indicative of something.