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Clarification on the Decimal type in Python

stackoverflow.com › questions › 20354423 › clarification-on-the-decimal-type-in-python

The Decimal class is best for financial type addition, subtraction multiplication, division type problems:

>>> (1.1+2.2-3.3)*10000000000000000000
4440.892098500626                            # relevant for government invoices...
>>> import decimal
>>> D=decimal.Decimal
>>> (D('1.1')+D('2.2')-D('3.3'))*10000000000000000000
Decimal('0.0')

The Fraction module works well with the rational number problem domain you describe:

>>> from fractions import Fraction
>>> f = Fraction(1) / Fraction(3)
>>> f
Fraction(1, 3)
>>> f * 3 < 1
False
>>> f * 3 == 1
True

For pure multi precision floating point for scientific work, consider mpmath.

If your problem can be held to the symbolic realm, consider sympy. Here is how you would handle the 1/3 issue:

>>> sympy.sympify('1/3')*3
1
>>> (sympy.sympify('1/3')*3) == 1
True

Sympy uses mpmath for arbitrary precision floating point, includes the ability to handle rational numbers and irrational numbers symbolically.

Consider the pure floating point representation of the irrational value of √2:

>>> math.sqrt(2)
1.4142135623730951
>>> math.sqrt(2)*math.sqrt(2)
2.0000000000000004
>>> math.sqrt(2)*math.sqrt(2)==2
False

Compare to sympy:

>>> sympy.sqrt(2)
sqrt(2)                              # treated symbolically
>>> sympy.sqrt(2)*sympy.sqrt(2)==2
True

You can also reduce values:

>>> import sympy
>>> sympy.sqrt(8)
2*sqrt(2)                            # √8 == √(4 x 2) == 2*√2...

However, you can see issues with Sympy similar to straight floating point if not careful:

>>> 1.1+2.2-3.3
4.440892098500626e-16
>>> sympy.sympify('1.1+2.2-3.3')
4.44089209850063e-16                   # :-(

This is better done with Decimal:

>>> D('1.1')+D('2.2')-D('3.3')
Decimal('0.0')

Or using Fractions or Sympy and keeping values such as 1.1 as ratios:

>>> sympy.sympify('11/10+22/10-33/10')==0
True
>>> Fraction('1.1')+Fraction('2.2')-Fraction('3.3')==0
True

Or use Rational in sympy:

>>> frac=sympy.Rational
>>> frac('1.1')+frac('2.2')-frac('3.3')==0
True
>>> frac('1/3')*3
1

You can play with sympy live.

Answer from dawg on Stack Overflow

Python

docs.python.org › 3 › library › decimal.html

decimal — Decimal fixed-point and floating-point arithmetic

Note Decimal.from_float(0.1) is ...51231257827021181583404541015625. ... From Python 3.2 onwards, a Decimal instance can also be constructed directly from a float....

Real Python

realpython.com › ref › stdlib › decimal

decimal | Python Standard Library – Real Python

>>> from decimal import Decimal >>> Decimal("0.1") + Decimal("0.2") Decimal('0.3') >>> # Using the built-in float >>> 0.1 + 0.2 0.30000000000000004

Discussions

Newbie question about 'decimal' calculations

hi @ all, shortly learned that python is using ‘mpdecimal’ for the decimal module, and now that mpdecimal doesn’t provide some functions, e.g. cbrt, trigonometrics, exp10 and so on, am I right in assumption calculations for such are performed in binary and the converted to decimal results? More on discuss.python.org

discuss.python.org

0

2

January 16, 2025

Clarification on the Decimal type in Python - Stack Overflow

Everybody knows, or at least, every programmer should know, that using the float type could lead to precision errors. However, in some cases, an exact solution would be great and there are cases wh... More on stackoverflow.com

stackoverflow.com

What's different between Decimal and Floating point numbers in Python?

Python's integers (±0, 1, 2, etc.) have unlimited accuracy, which is unusual as far as programming languages go. In most languages they usually cap at 64-bits (aka long int) and there may be multiple integer types of various sizes. This makes Python very useful for scientific computing as you don't need a separate BigNum library to handle arbitrary precision. Python's floating-point numbers don't quite have this same luxury due to the inaccurate nature of them. Since many decimal numbers cannot be accurately represented in binary, floating-point math will always run into inaccuracies. For instance, 0.1 + 0.1 + 0.1 isn't 0.3, but something like 0.3000000000001. You'll use floats whenever whole numbers aren't enough, but you don't need a specific amount of accuracy. You probably never meant to ask about this, but decimal.Decimal is an alternative to float that lets you set its precision yourself. It's still not infinitely accurate, but it's often used in scientific computing where integers just can't cut it. More on reddit.com

r/learnpython

6

5

March 5, 2021

How do you get a decimal in python? - Stack Overflow

In a truly surreal experience, I have spent 20 minutes on a task I thought would take 20 seconds. I want to use decimals with 3 or more places. I cannot get anything over 1 place, and even in that... More on stackoverflow.com

stackoverflow.com

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Python - Binary to Decimal Conversion - YouTube

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View all

TutorialsPoint

tutorialspoint.com › decimal-functions-in-python

Decimal Functions in Python

July 30, 2019 - In Python, there is a module called Decimal, which is used to do some decimal floating point related tasks. This module provides correctly-rounded floating point arithmetic. To use it at first we need to import it the Decimal standard libra

W3Schools

w3schools.com › python › ref_module_decimal.asp

Python decimal Module

Python Examples Python Compiler Python Exercises Python Quiz Python Challenges Python Server Python Syllabus Python Study Plan Python Interview Q&A Python Bootcamp Python Certificate Python Training ... from decimal import Decimal print(Decimal('0.1') + Decimal('0.2')) print(Decimal('1') / Decimal('4')) Try it Yourself »

Python.org

discuss.python.org › python help

Newbie question about 'decimal' calculations - Python Help - Discussions on Python.org

January 16, 2025 - hi @ all, shortly learned that python is using ‘mpdecimal’ for the decimal module, and now that mpdecimal doesn’t provide some functions, e.g. cbrt, trigonometrics, exp10 and so on, am I right in assumption calculations for such are performed in binary and the converted to decimal results?

W3Schools

w3schools.com › python › python_numbers.asp

Python Numbers

Float, or "floating point number" is a number, positive or negative, containing one or more decimals. ... Float can also be scientific numbers with an "e" to indicate the power of 10. ... x = 1 # int y = 2.8 # float z = 1j # complex #convert from int to float: a = float(x) #convert from float to int: b = int(y) #convert from int to complex: c = complex(x) print(a) print(b) print(c) print(type(a)) print(type(b)) print(type(c)) Try it Yourself » · Note: You cannot convert complex numbers into another number type. Python does not have a random() function to make a random number, but Python has a built-in module called random that can be used to make random numbers:

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GeeksforGeeks

geeksforgeeks.org › python › precision-handling-python

Precision Handling in Python - GeeksforGeeks

December 19, 2025 - Given a number, the task is to control its precision either by rounding it or formatting it to a specific number of decimal places. For Example: Input: x = 2.4 Output: Integral value = 2 Smallest integer greater than x = 3 Greatest integer smaller than x = 2 · Let's explore different ways to do this task in Python.

Stack Overflow

stackoverflow.com › questions › 20354423 › clarification-on-the-decimal-type-in-python

Clarification on the Decimal type in Python - Stack Overflow

Top answer

1 of 4

9

Integers (int type) are "whole numbers", without the fractional part, eg. 10. You use this type when the value is always an integer, e.g. a counter. Floating point numbers (float type) can have fractional part, e.g. 10.1234. They are stored using the closest representation in binary notation. Most numbers cannot be represented accurately, so they are slightly off. You use float for most mathematical calculations involving fractional numbers. Decimal numbers (Decimal type in Python) are used to represent floating point numbers accurately, with a defined precision (a defined number of places after decimal point). They are represented with two integer numbers, one for the integer part and one for the fractional part. For example. 10.1234 is stored as (10, 1234). Decimal type is required when fractional numbers must be represented accurately, with defined precision. The most notable example is financial calculations. Using float type you may get a result of a financial operation as 1010.123456$. But money is expressed with at most two decimal places. What does 0.123456$ mean? You can round it to 1010.12$, but then what happens with the remaining 0.003456$? Some "smart" programmers used that to their advantage in the past and they made a lot of money (which they eventually had to give back). So, for money calculations, you should use Decimal type. A good explanation of the Decimal type is in the documentation: https://docs.python.org/3/library/decimal.html

2 of 4

7

Python's integers (±0, 1, 2, etc.) have unlimited accuracy, which is unusual as far as programming languages go. In most languages they usually cap at 64-bits (aka long int) and there may be multiple integer types of various sizes. This makes Python very useful for scientific computing as you don't need a separate BigNum library to handle arbitrary precision. Python's floating-point numbers don't quite have this same luxury due to the inaccurate nature of them. Since many decimal numbers cannot be accurately represented in binary, floating-point math will always run into inaccuracies. For instance, 0.1 + 0.1 + 0.1 isn't 0.3, but something like 0.3000000000001. You'll use floats whenever whole numbers aren't enough, but you don't need a specific amount of accuracy. You probably never meant to ask about this, but decimal.Decimal is an alternative to float that lets you set its precision yourself. It's still not infinitely accurate, but it's often used in scientific computing where integers just can't cut it.

DigitalOcean

digitalocean.com › community › tutorials › python-decimal-division-round-precision

Python decimal - division, round, precision | DigitalOcean

August 4, 2022 - Python decimal module helps us in division with proper precision and rounding of numbers.

Medium

pranaysuyash.medium.com › how-i-lost-10-000-because-of-a-python-float-and-how-you-can-avoid-my-mistake-3bd2e5b4094d

Python Decimal vs Float: The $10,000 Mistake to Avoid | Medium

April 9, 2025 - Discover why using Python's float for financial calculations can be disastrous, and learn how to properly handle money with the Decimal module to avoid costly errors.

SSOJet

ssojet.com › binary-encoding-decoding › decimal-in-python

Decimal in Python | Binary to Text Encodings in Programming Languages

To work with precise decimal numbers in Python, you must first import the Decimal type from the decimal module. The most reliable way to create a Decimal object is by initializing it from a string.

Shiksha

shiksha.com › home › it & software › it & software articles › programming articles › precision handling in python

Precision Handling in Python - Shiksha Online

October 31, 2022 - The format() function in python can be used to format a float value for precision based on the format specifier. ... format_specifier: The format specifier in the above syntax specifies how the value is to be formatted.

Python Tutorial

pythontutorial.net › home › advanced python › python decimal

An Essential Guide to Python Decimal By Examples

February 26, 2021 - Unlike floats, Python represents decimal numbers exactly. And the exactness carries over into arithmetic.

Stack Overflow

stackoverflow.com › questions › 11488523 › how-do-you-get-a-decimal-in-python

How do you get a decimal in python? - Stack Overflow