More Intuitive Calculator Arithmetic (2018) (opens in new tab)

    >>> import fractions
    >>> from fractions import Fraction as F
    >>> F(3, 17) * F(12, 5) + F(56, 99)
    Fraction(8324, 8415)
    >>> F(3, 17) * F(12, 5) + F(56, 99) / 3 + 2 * 4
    Fraction(217412, 25245)

    >>> F(217412, 25245) + 0.1
    8.712081600316894
    >>> F(217412, 25245) + 1j
    (8.612081600316895+1j)

    >>> import math
    >>> math.pi
    3.141592653589793
    >>> math.e
    2.718281828459045

https://docs.perl6.org/language/numerics#Rational

Author here. The paraphrase makes this sound wrong, but what I actually meant is that I don’t know of any calculator that uses rationals while the numerator and denominator can be represented as integer floating point doubles, and then falls back to a single floating point double if the numerator or denominator overflow.

I am aware of many systems that use arbitrary precision rationals, and I mentioned this in the post:

> Rational numbers where the numerator and denominator are allowed to grow arbitrarily large are used by computer algebra systems (CAS) like Mathematica and Maple (and also some high-end handheld graphing calculators).

  :; sbcl
  This is SBCL 1.5.5, an implementation of ANSI Common Lisp.
  ...
  * (/ 1 3)
  1/3

However, if you input a number containing a decimal point it will be represented as a floating point number and performing arithmetic between that and a rational will cause the rational to be coerced to a floating point number and yield a floating point result. (If you're working with a more complicated expression, you can sometimes end up with some terms/coefficients of the expression being rational numbers and some being floats, until you ask for the expression to be fully evaluated down to a numerical result.)