Rational or Irrational Calculator

Type a number and this tool says whether it is rational or irrational, and why. A fraction, a terminating decimal or a repeating decimal written as 0.8(3) comes back rational with the exact fraction and the subtraction that produces it; a symbolic form such as sqrt(2), cbrt(9), pi, e or phi comes back irrational with the theorem that settles it named. It is explicit about the difference: for sqrt(2) the argument is a proof about integers, while for a typed string of digits the answer is only a reading of that string, since every finite decimal is rational no matter what number it was truncated from. A second tab divides out any fraction and finds the repeating block, showing the remainder cycle that proves a fraction can never expand without a pattern.