Base 2 doesn’t work well with military too:

http://www-users.math.umn.edu/~arnold/disasters/patriot.html

Doing calculations with an exact number type such as [big] rationals, and then explicitly converting to floating point or rounding/truncating digits of precision as needed, is a pretty good middle ground for many applications. 109/100 − 109375/100000 = 109/100 − 35/32 = −3/800 = −3.75ᴇ−3.

An easier example: type this in your browser console:

0.1 + 0.2 == 0.3

false!(?)