But there was a big issue that we didn't anticipate. During the course of a simple program it was quite common for calculations to slow down dramatically, because numbers with ever-larger numerators and denominators were being computed (and rational arithmetic quickly slows down as those get bigger). So e.g. you might be computing your taxes with a precision of a million digits -- only to be rounding them down to dollars for display.

(Quote by Guido van Rossum)

Decimal can still violate all the invariants that binary floats can. Binary has better approximation properties if you care about the *degree* of inexactness rather than the *frequency*[1] of inexactness. Fractions can quickly become very inefficient.

(Quote by Stephen J. Turnbull) I have a solution. To add, we convert to decimal and then add, then change back to fraction. If we have hard-to-represent decimals like 1 / 3, we can add with numerators. Hybrid additions. This could really speed up things... -- -Surya Subbarao