Table of Contents
Python as a Calculator
Python contains functions found in any standard graphing calculator. An arithmetic operation is either addition, subtraction, multiplication, division, or powers between two numbers. An arithmetic operator is a symbol that Python reserves to mean one of the aforementioned arithmetic operations. These symbols are
+
for addition
for subtraction*
for multiplication/
for division**
for exponentiation.
Example
Let’s look at a few examples.11+2 # addition
3
12**3 # exponentiation
8
13/4 # division
0.75
Note that the hash key #
precedes a comment which will be ignored by the Python compiler.
Order of Operations
An ‘order of operations’ is a standard order of precedence that different operations have in relationship to one another. Python also uses a similar type of rule known as PEMDAS ^{1}. Powers are executed before multiplication and division, which are executed before addition and subtraction.
 P – Parentheses
 E – Exponentiation
 M – Multiplication
 D – Division
 A – Addition
 S – Subtraction
The precedence of operators above is listed from High to low. For M and D, we perform (M)ultiplication or (D)ivision from left to right based on whichever operation comes first. Similarly, for A and S, we perform (A)ddition or (S)ubtraction from left to right based on whichever operation comes first.
Example
The following illustrates the fact that if M and D appear together without any parentheses, the order of operations will be from left to right.142/7*2
12.0
However, it is always best to always use parentheses to precisely define the order you desire.
Example
Compute $$\frac{2 \times 3}{2^2 + \frac{6}{3} }$$1(2*3)/(2**2 + 6/3)
1.0
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Mathematical Functions
Python has many basic mathematical functions like sin
, cos
, tan
, asin
, acos
, atan
, exp
, log
, log10
and sqrt
stored in a module (explained in a later section) called math
. To access these functions, we need to first import this module.
1import math
After importing the math
module, we can now access the various math functions by typing math
followed by a dot and the function desired.
Example
To compute $ \sqrt{16} = 4 $.1math.sqrt(16)
4.0
Example
To compute $ \cos{\pi} = 1.0 $.1math.cos(math.pi)
1.0
Example
To compute $e ^{\ln(5)}$.1math.exp(math.log(5))
4.999999999999999
Note that the result above is not 5.0 exactly due to Python’s inherent floatingpoint approximation. Also, the log
function in Python refers to the natural logarithm. To compute the logarithm of a number ($a$) to any base, we use log(a,base)
.
Example
To compute $\log_2 8$.1math.log(8,2)
3.0
Example
Division $\frac{17}{3}$.117 / 3 # classic division returns a float
5.666666666666667
Example
Floor division.117 // 3 # floor division discards the fractional part
5
Example
The following computes the remainder when 10 is divided by 3.1math.remainder(10,3)
1.0
An alternative syntax is
110 % 3
1
where %
is called the modulo symbol.
The complete list of Python’s math functions can be found here
. Another way to see all available math functions is to type math
followed by a dot and the tab key.

PEDMAS is typically introduced in a course on precalculus. ↩︎