It's not "round off error", though. More like:
"It's a base 2 fractional number with no exact decimal expansion with a finite number of digits. Display it in base 2 fractional form if you don't want to see an approximation."
"It's a base 2 fractional number with no exact decimal expansion with a finite number of digits. Display it in base 2 fractional form if you don't want to see an approximation."
Binary numbers are a countably infinite set. Decimal numbers are a countably infinite set. You can therefore map binary representation to decimal representation 1-1 with a simple mapping function.
OTOH, floating point numbers are an uncountably infinite set. The only way to map binary numbers to floating point numbers is to map to a strict subset.
The subset happens to be different when mapping binary to floating point and decimal to floating point when using IEEE754.
Anyway, mathematicians don't use numbers at all - debasing the equations by performing caculations with them is so.. gauche. Leave that to the physicists, chemists and engineers.
We'd rather calculate with knows than numbers. (See http://en.wikipedia.org/wiki/Knot_theory)