Then, would it be better to store rationals as 2 ints with understood division, and irrationals as 2 ints as understood powers? Why are we working with these n

Then, would it be better to store rationals as 2 ints with understood division, and irrationals as 2 ints as understood powers? Why are we working with these numbers so imprecisely, and with such discontinuity? When I've done math work in school, I always worked with the primitives without approximating.. 2^.5 was handled as such unless asked for an approximate answer. I also ran across this in AutoCAD. Because they force arbitrary precision, one cannot define a sqrt length. 1.414 doesn't reach all the way on a r-triangle with 1,1 .