Python as a Calculator

Arithmetic Operators

Operator Operation Expression English description Result
+ addition 11 + 56 11 plus 56 67
- subtraction 23 - 52 23 minus 52 -29
* multiplication 4 * 5 4 multiplied by 5 20
** exponentiation 2 ** 5 2 to the power of 5 32
/ division 9 / 2 9 divided by 2 4.5
// integer division 9 // 2 9 divided by 2 4
% modulo (remainder) 9 % 2 9 mod 2 1

Types int and float

type is a set of values and operations that can be performed on those values.

Two of Python's numeric types:

  • int: integer
    For example: 348940-3-18

  • float: floating point number (an approximation to a real number)
    For example: 5.67.34253452.00.0-89.34-9.5

Arithmetic Operator Precedence

When multiple operators are combined in a single expression, the operations are evaluated in order of precedence.

Operator Precedence
** highest
- (negation)  
*, /, //, %  
+ (addition), - (subtraction) lowest

Syntax and Semantics

Syntax: the rules that describe valid combinations of Python symbols

Semantics: the meaning of a combination of Python symbols is the meaning of an instruction — what a particular combination of symbols does when you execute it.


A syntax error occurs when we an instruction with invalid syntax is executed. For example:

>>> 3) + 2 * 4
SyntaxError: invalid syntax

A semantic error occurs when an instruction with invalid semantics is executed. For example:

>>> 89.4 / 0
Traceback (most recent call last):
  File "", line 1, in
    89.4 / 0
ZeroDivisionError: float division by zero



Computer Memory

You may think of computer memory as a long list of storage locations where each location is identified with a unique number and each location houses a value. This unique number is called a memory address. Typically, we will write memory addresses as a number with an "id" as a prefix to distinguish them from other numbers (for example, id201 is memory address 201).

Variables are a way to keep track of values stored in computer memory. variable is a named location in computer memory. Python keeps variables in a separate list from values. A variable will contain a memory address, and that memory address contains the value. The variable then refers to the value. Python will pick the memory addresses for you.


A value has a memory address.
A variable contains a memory address.
A variable refers to a value.
A variable points to a value.

Example: Value 8.5 has memory address id34.
Variable shoe_size contains memory address id34.
The value of shoe_size is 8.5.
shoe_size refers to value 8.5.
shoe_size points to value 8.5.


 Assignment statements

The general form of an assignment statement:

variable = expression

Example assignment statements:

>>> base = 20
>>> height = 12
>>> area = base * height / 2
>>> area

The rules for executing an assignment statement:

  1. Evaluate the expression. This produces a memory address.
  2. Store the memory address in the variable.

Variable names

The rules for legal Python names:

  1. Names must start with a letter or _.
  2. Names must contain only letters, digits, and _.

For Python, in most situations, the convention is to use pothole_case (or Snake Case) in Python: lowercase_words_separated_by_underscores


Function Call

The general form of a function call:


The rules for executing a function call:

  1. Evaluate the arguments.
  2. Call the function, passing in the argument values.


  • Argument: a value given to a function
  • Pass: to provide to a function
  • Call: ask Python to evaluate a function
  • Return: pass back a value

Example function calls:

>>> abs(-23)
>>> abs(56.24)

Function dir

Python has a set of built-in functions. To see the list of built-in functions, run dir(__builtins__):

>>> dir(__builtins__)< br/> ['ArithmeticError', 'AssertionError', 'AttributeError', 'BaseException', 'BufferError', 'BytesWarning', 'DeprecationWarning', 'EOFError', 'Ellipsis', 'EnvironmentError', 'Exception', 'False', 'FloatingPointError', 'FutureWarning', 'GeneratorExit', 'IOError', 'ImportError', 'ImportWarning', 'IndentationError', 'IndexError', 'KeyError', 'KeyboardInterrupt', 'LookupError', 'MemoryError', 'NameError', 'None', 'NotImplemented', 'NotImplementedError', 'OSError', 'OverflowError', 'PendingDeprecationWarning', 'ReferenceError', 'ResourceWarning', 'RuntimeError', 'RuntimeWarning', 'StopIteration', 'SyntaxError', 'SyntaxWarning', 'SystemError', 'SystemExit', 'TabError', 'True', 'TypeError', 'UnboundLocalError', 'UnicodeDecodeError', 'UnicodeEncodeError', 'UnicodeError', 'UnicodeTranslateError', 'UnicodeWarning', 'UserWarning', 'ValueError', 'Warning', 'ZeroDivisionError', '_', '__build_class__', '__debug__', '__doc__', '__import__', '__name__', '__package__', 'abs', 'all', 'any', 'ascii', 'bin', 'bool', 'bytearray', 'bytes', 'callable', 'chr', 'classmethod', 'compile', 'complex', 'copyright', 'credits', 'delattr', 'dict', 'dir', 'divmod', 'enumerate', 'eval', 'exec', 'exit', 'filter', 'float', 'format', 'frozenset', 'getattr', 'globals', 'hasattr', 'hash', 'help', 'hex', 'id', 'input', 'int', 'isinstance', 'issubclass', 'iter', 'len', 'license', 'list', 'locals', 'map', 'max', 'memoryview', 'min', 'next', 'object', 'oct', 'open', 'ord', 'pow', 'print', 'property', 'quit', 'range', 'repr', 'reversed', 'round', 'set', 'setattr', 'slice', 'sorted', 'staticmethod', 'str', 'sum', 'super', 'tuple', 'type', 'vars', 'zip']

Function help

To get information about a particular function, call help and pass the function as the argument. For example:

>>> help(abs)
Help on built-in function abs in module builtins:
    abs(number) -> number

    Return the absolute value of the argument.

Optional arguments

In the description of function pow below, the square brackets around [, z] indicate that the third argument is optional:

>>> help(pow)
Help on built-in function pow in module builtins:

    pow(x, y[, z]) -> number

    With two arguments, equivalent to x**y.  With three arguments,
    equivalent to (x**y) % z, but may be more efficient (e.g. for longs).

Function pow can be called with either two or three arguments:

>>> pow(2, 5)
>>> pow(2, 5, 3)

The general form of a function definition:

def function_name(parameters):

  • def: a keyword indicating a function definition
  • function_name: the function name
  • parameters:
    • the parameter(s) of the function, 0 or more and are separated by a comma
    • a parameter is a variable whose value will be supplied when the function is called
  • body:
    • 1 or more statements, often ending with a return statement

Example of a function definition:

def f(x):
    return x ** 2

return statement

The general form of a return statement:
return expression

The rules for executing a return statement:

  1. Evaluate the expression. This produces a memory address.
  2. Pass back that memory address to the caller. Exit the function.

Function Calls

Function calls are expressions and the result can be stored in a variable.

The general form of a function call:


The rules for executing a function call:
  1. Evaluate the arguments to produce memory addresses.
  2. Store those memory addresses in the corresponding parameters.
  3. Execute the body of the function.

Example of a function definition and function calls:
>>> def area(base, height):
    return base * height / 2
>>> area(3, 4)
>>> result = area(10, 7.45)
>>> result

Saving your programs to ".py" files

We usually save our Python programs in ".py" files. A file can contain multiple function definitions and other statements. Before calling a function from a ".py" file in the shell in IDLE, you need to first execute Run -> Run Module, or else the shell will not recognize the function call.