# Python Number Types: int, float, complex

Python supports three numeric types to represent numbers: integers, float, and complex number. Here you will learn about each number type.

## Int

In Python, integers are zero, positive or negative whole numbers without a fractional part and having unlimited precision, e.g. 0, 100, -10. The followings are valid integer literals in Python.

Example: Python Numbers
``````#integer variables
x = 0
print(x)

x = 100
print(x)

x = -10
print(x)

x = 1234567890
print(x)

x = 5000000000000000000000000000000000000000000000000000000
print(x)
``````

Integers can be binary, octal, and hexadecimal values.

Example: Python Numbers
``````b = 0b11011000 # binary
print(b)

o = 0o12 # octal
print(o)

print(h)
``````

All integer literals or variables are objects of the `int` class. Use the `type()` method to get the class name, as shown below.

Example: Python Numbers
``````print(type(100))

x=1234567890
print(type(x))

y=5000000000000000000000000000000000000000000000000000000
print(type(y))
``````

Note: Leading zeros in non-zero integers are not allowed in Python, e.g. 000123 is invalid number and 0000 becomes 0.

``````x=001234567890 #syntaxError: invalid token
``````

Python does not allow comma as number delimiter. Use underscore `_` as a delimiter instead.

Example: Number Delimiter
``````x = 1_234_567_890
print(x) #output: 1234567890
``````

Note that integers must be without a fractional part (decimal point). It it includes a fractional then it becomes a float.

Example: Python Numbers
``````x=5
print(type(x)) #output: <class 'int'>

x=5.0
print(type(x)) #output: <class 'float'>
``````

The `int()` function converts a string or float to int.

Example: int() Function
``````x = int('100')
print(x) #output: 100

y = int('-10')
print(y) #output: -10

z = int(5.5)
print(z) #output: 5

n = int('100', 2)
print(n) #output: 4
``````

### Binary

A number having 0b with eight digits in the combination of 0 and 1 represent the binary numbers in Python. For example, 0b11011000 is a binary number equivalent to integer 216.

Example: Binary Numbers
``````x = 0b11011000
print(x)

x = 0b_1101_1000
print(x)
print(type(x))
``````

### Octal

A number having 0o or 0O as prefix represents an octal number. For example, 0O12 is equivalent to integer 10.

Example: Octal Numbers
``````x = 0o12

print(x)
print(type(x))
``````

A number with 0x or 0X as prefix represents hexadecimal number. For example, 0x12 is equivalent to integer 18.

``````x = 0x12

print(x)
print(type(x))
``````

## Float

In Python, floating point numbers (float) are positive and negative real numbers with a fractional part denoted by the decimal symbol `.` or the scientific notation `E` or `e`, e.g. 1234.56, 3.142, -1.55, 0.23.

Example: Float Numbers
``````f = 1.2
print(f) #output: 1.2
print(type(f)) #output: <class 'float'>

f=123_42.222_013 #output: 12342.222013
print(f)

f=2e400
print(f) #output: inf
``````

As you can see, a floating point number can be separated by the underscore `_`. The maximum size of a float is depend on your system. The float beyond its maximum size referred as inf, Inf, INFINITY, or infinity. For example, a float number `2e400` will be considered as infinity for most systems.

Scientific notation is used as a short representation to express floats having many digits. For example: 345.56789 is represented as 3.4556789e2 or 3.4556789E2

Example: Scienticific Numbers
``````f = 1e3
print(f) #output: 1000.0

f = 1e5
print(f) #output:100000.0

f = 3.4556789e2
print(f) #output:
print(type(f)) #output:345.56789
``````

Use the `float()` function to convert string, int to float.

Example: float() Function
``````f=float('5.5')
print(f) #output: 5.5

f=float('5')
print(f) #output: 5.0

f=float('     -5')
print(f) #output: -5.0

f=float('1e3')
print(f) #output: 1000.0

f=float('-Infinity')
print(f) #output: -inf

f=float('inf')
print(f)  #output: inf
print(type(f)) #output:<class 'float'>
``````

## Complex Numbers

A complex number is a number with real and imaginary components. For example, `5 + 6j` is a complex number where 5 is the real component and 6 multiplied by j is an imaginary component.

Example: Complex Numbers
``````a = 5+2j
print(a)
print(type(a))
``````

You must use j or J as imaginary component. Using other character will throw syntax error.

Example: Invalid Complex Numbers
``````a=5+2k
a=5+j
a=5i+2j
``````

## Arithmetic Operators

The following table list arithmetic operators on integer values:

Operator Description Example
+ (Addition) Adds operands on either side of the operator. a,b = 10, 20
print(a+b) #30
- (Subtraction) Subtracts the right-hand operand from the left-hand operand. a,b = 10, 20
print(a-b) #-10
* (Multiplication) Multiplies values on either side of the operator. a,b = 10, 20
print(a*b) #200
/ (Division) Divides the left-hand operand by the right-hand operand. a,b = 10, 20
print(b/a) #2.0
% (Modulus) Returns the remainder of the division of the left-hand operand by right-hand operand. a,b = 10, 22
print(a+b) #2
** (Exponent) Calculates the value of the left-operand raised to the right-operand. a=3
print(a**2) #9
print(a**3) #27
// (Floor Division) The division of operands where the result is the quotient in which the digits after the decimal point are removed. But if one of the operands is negative, the result is floored, i.e., rounded away from zero (towards negative infinity): a,b = 9, 2
print(a//b) #4

Try it

## Arithmetic Operations on Complex Numbers

Addition and subtraction of complex numbers is straightforward. Real and imaginary parts are added/subtracted to get the result.

Example: Arithmetic Operation on Complex Numbers
``````a=6+4j
b=3+2j

print("a+2=",a+2)
print("a*2=",a*2)
print("a/2=",a/2)
print("a**2=",a**2)
print("a+b=",a+b)
print("a-b=",a-b)
``````

As you can see in the above example, the arithmetic operators can also be used with two complex numbers.

The process of multiplying these two complex numbers is very similar to multiplying two binomials. Multiply each term in the first number by each term in the second number.

Example: Multiply Complex Numbers
``````a=6+4j
b=3+2j

c=a*b
print(c)

c=(6+4j)*(3+2j)
print(c)

c=(18+12j+14j+8*1)
print(c)
``````

## Numeric Functions

A numeric object of one type can be converted in another type using the following functions:

Built-in Function Description
int Returns the integer object from a float or a string containing digits.
float Returns a floating-point number object from a number or string containing digits with decimal point or scientific notation.
complex Returns a complex number with real and imaginary components.
hex Converts a decimal integer into a hexadecimal number with 0x prefix.
oct Converts a decimal integer in an octal representation with 0o prefix.
pow Returns the power of the specified numbers.
abs Returns the absolute value of a number without considering its sign.
round Returns the rounded number.
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