Numbers in

About Numbers

Python has three different types of built-in numbers: integers (int), floating-point (float), and complex (complex). Fractions (fractions.Fraction) and Decimals (decimal.Decimal) are also available via import from the standard library.

Whole numbers including hexadecimal (hex()), octal (oct()) and binary (bin()) numbers without decimal places are also identified as ints:

# Ints are whole numbers.
>>> 1234
1234
>>> type(1234)
<class 'int'>

>>> -12
-12

Numbers containing a decimal point (with or without fractional parts) are identified as floats:

>>> 3.45
3.45
>>> type(3.45)
<class 'float'>

Arithmetic

Python fully supports arithmetic between these different number types, and will convert narrower numbers to match their less narrow counterparts when used with the binary arithmetic operators (+, -, *, /, //, and %).

All numbers (except complex) support all arithmetic operations, evaluated according to operator precedence. Support for mathematical functions (beyond + and -) for complex numbers can be found in the cmath module.

Addition and subtraction

Addition and subtraction operators behave as they do in normal math. If one or more of the operands is a float, the remaining ints will be converted to floats as well:

>>> 5 - 3
2
# The int is widened to a float here, and a float is returned.
>>> 3 + 4.0
7.0

Multiplication

As with addition and subtraction, multiplication will convert narrower numbers to match their less narrow counterparts:

>>> 3 * 2
6

>>> 3 * 2.0
6.0

Division

Division always returns a float, even if the result is a whole number:

>>> 6/5
1.2

>>> 6/2
3.0

Floor division

If an int result is needed, you can use floor division to truncate the result. Floor division is performed using the // operator:

>>> 6//5
1

>>> 6//2
3

Modulo

The modulo operator (%) returns the remainder of the division of the two operands:

# The result of % is zero here, because dividing 8 by 2 leaves no remainder
>>> 8 % 2
0

# The result of % is 2 here, because 3 only goes into 5 once, with 2 left over
>>> 5 % 3
2

Another way to look at 5 % 3:

>>> whole_part = int(5/3)
1

>>> decimal_part = 5/3 - whole_part
0.6666666666666667

>>> whole_remainder = decimal_part * 3
2.0

Exponentiation

Exponentiation is performed using the ** operator:

>>> 2 ** 3
8

>>> 4 ** 0.5
2

Conversions

Numbers can be converted from int to floats and floats to int using the built-in functions int() and float():

>>> int(3.45)
3

>>> float(3)
3.0

Round

Python provides a built-in function round(number, <decimal_places>) to round off a floating point number to a given number of decimal places. If no number of decimal places is specified, the number is rounded off to the nearest integer and will return an int:

>>> round(3.1415926535, 2)
3.14

>>> round(3.1415926535)
3

Priority and parentheses

Python allows you to use parentheses to group expressions. This is useful when you want to override the default order of operations.

>>> 2 + 3 * 4
14

>>> (2 + 3) * 4
20

Python follows the PEMDAS rule for operator precedence. This means calculations within () have the highest priority, followed by **, then *, /, //, %, +, and -:

>>> 2 + 3 - 4 * 4
-11

>>> (2 + 3 - 4) * 4
4

# In the following example, the `**` operator has the highest priority, then `*`, then `+`
# Meaning we first do 4 ** 4, then 3 * 256, then 2 + 768
>>> 2 + 3 * 4 ** 4
770

Precision & Representation

Integers in Python have arbitrary precision -- the number of digits is limited only by the available memory of the host system.

Floating point numbers are usually implemented using a double in C (15 decimal places of precision), but will vary in representation based on the host system. Complex numbers have a real and an imaginary part, both of which are represented by floating point numbers.

For a more detailed discussions of the issues and limitations of floating point arithmetic across programming languages, take a look at 0.30000000000000004.com and The Python Tutorial.