How to calculate and store the number in scientific notation?

I am using Python to model the statistical physical, so I will deal with small numbers.

For example,

a = 2.22e-300, b = 3e-200

and I want to calculate

a * b = 6.66e-500.

However, in Python 3 it shows 0.0.

I am thinking to design a data type: the first part to store the float number, which is 6.66 here, and the second part stores the magnitude, which is -500.

May I ask how I can implement this? Or is there any better way to deal with the scientific number?

Solution

Create a class:

class Sci_note:
    def __init__(self, base, exp):
        self.base = base
        self.exp = exp
    def __mul__(self, other):
        return Sci_note(self.base * other.base,
                        self.exp + other.exp)
    def __str__(self):
        return str(self.base) + 'e' + str(self.exp)

and it functions as you would expect:

>>> a = Sci_note(2.22, -300)
>>> b = Sci_note(3, -200)
>>> c = a * b
>>> c.base
6.66
>>> c.exp
-500

update

I added a __str__ method (above), so they are displayed properly when printed:

>>> print(a)
2.22e-300

Of course, I have only implemented the multiplication method here, but I will leave it up to you to implement the others when required. It may be the case that you only need multiplication so I would be wasting everyone's time if I wrote them now!

In addition, creating a __float__ handler would also not be useful here, as Python can't handle floats of the order ^-300, so it would be useless to return them as we would just get 0!