I like how Haskell does it. When you simply write a number like "3" it will infer the type to be "Num a => a" which means it could be any type you have loaded that defines the functions in the typeclass Num:
class Num a where
(+) :: a -> a -> a
(-) :: a -> a -> a
(*) :: a -> a -> a
negate :: a -> a
abs :: a -> a
signum :: a -> a
fromInteger :: Integer -> a
"3.0" would be "Fractional a => a" which means it defines the functions in the typeclass Fractional (in addition to being a Num):
class Num a => Fractional a where
(/) :: a -> a -> a
recip :: a -> a
fromRational :: Rational -> a
Depending on how you use the value, the type would be further refined in compile-time. For example, if you did `recip 3`, 3 couldn't be any Num anymore, it would have to be some Fractional.
Regarding (5/3)*6, it does equal 10 using floating point. A better example would be how 0.1 + 0.2 is not equal to 0.3. We can see this:
ghci> 0.1 + 0.2 == (0.3 :: Float)
False
If we specified that we're working with Rational values, which are also Fractional a => a, and which are defined as a pair of integers, one representing a numerator and the other a denominator, roughly like so:
type Rational = Ratio Integer
data Ratio a = a :% a
then we can see that 0.1 + 0.2 does equal to 0.3:
ghci> 0.1 + 0.2 == (0.3 :: Rational)
True
It's pretty cool that Haskell lets you define new types of numbers and use them like any other. While you can transparently support hardware type numbers, represented by types like Int, Float, Double, Word, Word8, Word16, Word32, Word64, you also have transparent support for arbitrary precision Integer and Rational. Writing your functions to work with the typeclasses like Num and Fractional lets your functions work with any of these types and future types defined.