Why is the precision accurate when Decimal() takes in a string instead of float? in Python

Question

Why are these values different and how does it differ from each other?

>>> from decimal import Decimal
>>> Decimal('0.1') + Decimal('0.1') + Decimal('0.1') - Decimal('0.3')
Decimal('0.0')

>>> Decimal(0.1) + Decimal(0.1) + Decimal(0.1) - Decimal(0.3)
Decimal('2.775557561565156540423631668E-17')

Because *a `float` is inherently imprecise*. That is *why `decimal.Decimal` exists in the first place* — juanpa.arrivillaga, Apr 19 '19 at 01:21
(won't reopen without discussion) I disagree this is a duplicate. The question is why is the precision accurate when `Decimal()` takes in a string — TerryA, Apr 19 '19 at 01:21
Have you tried to do `Decimal("0.1") == 0.1` and `Decimal(0.1) == 0.1`? — ggrelet, Apr 19 '19 at 01:22
The precision is already lost when you represent a number with a floating point, and passing an imprecise number to the `Decimal` constructor will not recover the lost precision. — blhsing, Apr 19 '19 at 01:23
Possible duplicate of [Is floating point math broken?](https://stackoverflow.com/questions/588004/is-floating-point-math-broken) — Wai Ha Lee, Apr 19 '19 at 01:44

Mahmoud Elshahat · Accepted Answer · 2019-04-19T03:45:00.333

This is quoted from Decimal module source code which explains pretty good, if the input is float, the module internally calls the class method "Decimal.from_float()":

Note that Decimal.from_float(0.1) is not the same as Decimal('0.1'). Since 0.1 is not exactly representable in binary floating point, the value is stored as the nearest representable value which is 0x1.999999999999ap-4. The exact equivalent of the value in decimal is 0.1000000000000000055511151231257827021181583404541015625.

score 0 · Answer 2 · answered Apr 19 '19 at 01:26

When you pass '0.1' as string, the decimal is converted to a float, without losing precision, but it loses precision when you pass the float directly as 0.1, as you can see below

>>> Decimal(0.1)
Decimal('0.1000000000000000055511151231257827021181583404541015625')
>>> Decimal('0.1')
Decimal('0.1')

This then leads to all sort of wierd results

>>> Decimal(0.3) - Decimal(0.1) + Decimal(0.1) + Decimal(0.1)
Decimal('0.3999999999999999944488848768')

Why is the precision accurate when Decimal() takes in a string instead of float? in Python

2 Answers2

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