Decimal Library for Changing Number Precision in Python

The built in math functions in Python use binary approximations, giving some funky results when dealing with numbers containing decimals:

>>> .1+.2
0.30000000000000004
>>> round(100.00/3.000,4)
33.333300000000001

One way to appropriately find the sum of decimals is to use strings

>>> str(.1+.2)
'0.3'

Also, the default is to round to the nearest whole number when dividing

>>> 1/3
0
>>> 100/3
33

The decimal library is a useful tool for floating point arithmetic. Instead of the command 'from decimal import *' that would import everything from decimal, all I need to import is Decimal and getcontext. When importing modules, simplicity is preferred. There are less problems with naming in your code and you can be more aware of the tools at your disposal. I already imported decimal and looked through the directory to determine which modules I wanted. I'm only going to show the precision feature of decimal. You may want to import the entire library if you want to use other functions.

>>> from decimal import getcontext
>>> from decimal import Decimal
>>> getcontext()
Context(prec=28, rounding=ROUND_HALF_UP, Emin=-999999999, 
Emax=999999999, capitals=1, flags=[Inexact, Rounded], 
traps=[DivisionByZero, Overflow, InvalidOperation])
>>> #our precision is also known as significant figures, 
applied after arithmetic 
... #let's change our precision
... 
>>> getcontext().prec=6
>>> Decimal('1')/Decimal('7') #can be performed to strings
Decimal('0.142857')
>>> Decimal(1)/Decimal(7) #can be performed to integers
Decimal('0.142857')
>>> Decimal(10)/Decimal(7)
Decimal('1.42857') #notice that 6 is the total number of 
figures, not the number after the decimal
>>> Decimal(10)/Decimal(5)
Decimal('2') #not '2.00000,' which is considered more 
accurate than 2 by the science community

As someone with a science background, I found the decimal library's use of 'significant figures' interesting. Decimal can also be used in financial reporting or billing. You can also find maximums and minimums, change rounding properties, and do anything that you can do with the math library. I personally prefer the math library for the algebraic functions performed by decimal, because math's syntax is simpler. To learn more about decimal, click here .

Math with Python

If this is your first time using Python in Windows, you will have to download it from python.org. Every operating system includes a terminal, which we will be using to practice and test. Google "How to open terminal" and your operating system name to find specific information about opening your terminal. You will also need either VIM, WING, Eclipse, or another editor to save and run your programs, though we do not need to use it for this tutorial. This article will focus on math capabilities within Python, either performing calculations as a common calculator or within logic commands. So open your terminal and play with me.

I start my code with telling my terminal that I would be working in python. [gypsychemist@inspidell ~]$ is my shell prompt, "python" is what I typed, and the next three lines are showing that python is installed and open for me to use.

[gypsychemist@inspidell ~]$ python
Python 2.6.4 (r264:75706, Jun  4 2010, 18:20:16) 
[GCC 4.4.4 20100503 (Red Hat 4.4.4-2)] on linux2
Type "help", "copyright", "credits" or "license" for more
information.
>>> 3+2
5
>>> 3*2
6
>>> 6/2
3
>>> 3-2
1
>>> 3*(3-1)
6 
>>> pi=3.14
>>> 3*pi
9.4199999999999999
>>> abs(2-3)
1
>>> pow(3,2)
9
>>> 3**2
9
>>> 

Basic math commands are shown above. '+' is for addition, '-' for subtraction. '*' for multiplication, and '/' for division. The basic math rules regarding parenthesis and order of operations are followed correctly. You can also store numbers as words or letters to perform math equations on, such as the example with pi. In Python, '=' is used to assign and does not imply equivalency. The absolute value function and two alternative ways to find a number with an exponent (also known as power) are shown.

A useful tool in python is the math library. To see the functions you can use within math, type 'import math' and 'dir(math)' on the next line. You just told the terminal you are opening the library and viewing the directory. The terminal will show you the commands including different trigonometric functions, advanced algebra, and rounding options. To learn more about a command (such as floor rounding), you can type 'help(math.floor)'. Press 'q' to exit help.

>>> import math
>>> dir(math)
['__doc__', '__file__', '__name__', '__package__', 'acos', 'acosh', 
'asin', 'asinh', 'atan', 'atan2', 'atanh', 'ceil', 'copysign','cos', 
'cosh', 'degrees', 'e', 'exp', 'fabs', 'factorial', 'floor', 'fmod', 
'frexp', 'fsum', 'hypot', 'isinf', 'isnan', 'ldexp', 'log', 'log10', 
'log1p', 'modf', 'pi', 'pow', 'radians', 'sin', 'sinh', 'sqrt', 
'tan', 'tanh', 'trunc']
>>> help(math.floor)
>>> math.floor(4.5)
4.0

You can also test to determine if one number is divisible by another, such as when you want to execute commands on only the even indexes in a list. To determine if 3 is evenly divisible by 2, type '3 %2'. Python returns '1' because there is a remainder of 1 when you divide 3 by 2. If 0 is a result, then numbers are evenly divisible.

>>> 3%2
1
>>> 3%3
0

If given a list of numbers and you want to perform math functions such as adding the numbers together, you can use a for loop. Follow the below example:

>>> list=[2,3,6,7,4,6]
>>> sum=0
>>> for x in list:
...   sum+=x
... 
>>> sum
28
>>> 

In Python, spacing of indentions and capitalization are very important. After any statement ending with ':' , indent by a consistent amount (two spaces, four spaces, tab, your choice).'sum+=x' is the same as 'sum=sum+x'. 'x' is the value at the index as it goes through the list. So this code just said 0+2+3+6+7+4+6=28. Now that you understand how to do it with a basic for loop, the quicker way is to use the built in sum function. Because I used the variable 'sum', already, I need to first reinstate sum to its built in function.

>>> from __builtin__ import sum
>>> sum(list)
28

Using built in functions as variables should be avoided. As you learn more Python, you will learn safe and understandable variables to use in your code. For more information on numbers and math, you can visit http://docs.python.org/library/numeric.html