Why decimals do not interoperate with floats

Question

Notes on Decimal says:

## Decimal has all of the methods specified by the Real abc, but it should
## not be registered as a Real because decimals do not interoperate with
## binary floats (i.e.  Decimal('3.14') + 2.71828 is undefined).  But,
## abstract reals are expected to interoperate (i.e. R1 + R2 should be
## expected to work if R1 and R2 are both Reals).

I don't understand why Decimal('3.14') + 2.71828 is undefined. Decimal can be constructed from a float so I think that __add__ can be implemented as follows:

def __add__(self, other):
    if isinstance(other, float):
        return self + Decimal(other)
    ...

With it we will be able to get Decimal('3.14') + 2.71828 = Decimal('3.14') + Decimal(2.71828) = 5.858280000000000153903556566

Can you explain why they do not interoperate in current implementation?

EDIT: it is possible to save precision when converting float to decimal with converting it to str first:

def __add__(self, other):
    if isinstance(other, float):
        return self + Decimal(str(other))
    ...

Thus Decimal('3.14') + 2.71828 = Decimal('3.14') + Decimal('2.71828') = 5.85828 without losing precision.

Answer 1

The key is in the way that the Decimal is initialized.

Notice how in all the examples in the documentation, Decimal is made from a string. It allows us to pass a number without loosing precision when storing it.

number = Decimal('1.1')
print(number)

The output of the code above will always be Decimal('1.1')

Altough initalizing Decimal with a float is possible, we lose the very thing we want to achieve by using Decimal in the first place, precision. Consider the following line of code.

number = Decimal(1.1)

What's the values inside the number? In my instance, the output is

Decimal('1.100000000000000088817841970012523233890533447265625')

1.1 is stored in a float, which means it loses precision. Then we use that to initialize a Decimal. That's why you should be initializing Decimals using string, not float, to avoid losing precision, which is the whole point of using Decimal in the first place anyways.