python - Significant figures in the decimal module

Question

So I've decided to try to solve my physics homework by writing some python scripts to solve problems for me. One problem that I'm running into is that significant figures don't always seem to come out properly. For example this handles significant figures properly:

from decimal import Decimal
>>> Decimal('1.0') + Decimal('2.0')
Decimal("3.0")

But this doesn't:

>>> Decimal('1.00') / Decimal('3.00')
Decimal("0.3333333333333333333333333333")

So two questions:

1. Am I right that this isn't the expected amount of significant digits, or do I need to brush up on significant digit math?
2. Is there any way to do this without having to set the decimal precision manually? Granted, I'm sure I can use numpy to do this, but I just want to know if there's a way to do this with the decimal module out of curiosity.

Answer 1

Changing the decimal working precision to 2 digits is not a good idea, unless you absolutely only are going to perform a single operation.

You should always perform calculations at higher precision than the level of significance, and only round the final result. If you perform a long sequence of calculations and round to the number of significant digits at each step, errors will accumulate. The decimal module doesn't know whether any particular operation is one in a long sequence, or the final result, so it assumes that it shouldn't round more than necessary. Ideally it would use infinite precision, but that is too expensive so the Python developers settled for 28 digits.

Once you've arrived at the final result, what you probably want is quantize:

>>> (Decimal('1.00') / Decimal('3.00')).quantize(Decimal("0.001"))
Decimal("0.333")

You have to keep track of significance manually. If you want automatic significance tracking, you should use interval arithmetic. There are some libraries available for Python, including pyinterval and mpmath (which supports arbitrary precision). It is also straightforward to implement interval arithmetic with the decimal library, since it supports directed rounding.

You may also want to read the Decimal Arithmetic FAQ: Is the decimal arithmetic ‘significance’ arithmetic?