It's very much not the same as floating point. It is not faster, but you can represent any rational number exactly, which is impossible with floating point numbers. The idea is to use rationals for any exact, rational and use floating point for irrational and imprecise numbers.
Exactly. Perhaps 1/3 would have been a better example, since it can't be expressed exactly in either decimal or binary as a floating point number, but can be stored as a rational number by keeping the numerator and denominator separate. New programmers expect 1/3 + 1/3 + 1/3 to equal 1, but that's not guaranteed when using floating point. Indeed, Python claims that 1/3 * 5 != 5/3, due to floating-point rounding errors.
Some languages contain rational numbers in their standard. One of those is Common Lisp and dividing two non-floats (of whatever precision) always yields a rational number there (the integer type is a subtype of the rational type).
Ooh, nice. It turns out that Python does have an implementation in fraction.Fraction, but it's not used for native divisions. The the real issue is speed, particularly when adding or subtracting, but it would be much nicer to use float() or // when that's really important than to use Decimal() or Fraction() all over the place when correctness is important. Using float by default is premature optimization.
I don't see how floating point is more accurate than rationals for irrational numbers. Both are only capable of representing approximations.
The reason for switching to floating point for irrational numbers is for speed, not accuracy. Rationals are incapable of expressing irrational numbers directly, because they store their numerator and denominator as integers. Yes, it's possible to approximate an irrational number with a sufficiently large denominator, but that doesn't buy you any correctness, so you can switch to a faster floating point representation without surprising your users. At that point, using a different type can also let the program know, if it cares, whether a given number is exact.