## Numbers. Representation of numbers of different types. Basic numeric types. Number conversion functions

### Contents

- 1. Categories of numeric types
- 2. List of numeric types
- 3. Representation of integers (literals) in different calculus systems.
**Example** - 4. Types of integers in Python 2.6: regular and long. Example
- 5. Representation of integers in Python 3.0
- 6. Conversion functions of the numbers in the string, and vice versa hex(), oct(), bin(), int().
**Examples** - 7. Representation of real numbers.
**Example** - 8. Complex numbers.
**Examples** - 9. Creating complex numbers. Function complex().
**Example** **Related topics**

##### 1. Categories of numeric types

In Python, number types are represented by the following categories:

- ordinary numeric types (real, integer);
- literals (create numeric types);
- expressions (processing of numeric types).

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##### 2. List of numeric types

The following numeric types are supported in Python:

- integers and real numbers;
- complex numbers;
- fixed precision numbers;
- rational numbers;
- sets
- logical values;
- integers of unlimited precision.

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##### 3. Representation of integers (literals) in different calculus systems. Example

Integers (or integer literals) can be written in different calculus systems:

- decimal format;
- hexadecimal;
- octal;
- binary.

**Example**. Writing the number (literal) 30 in various formats

30 # decimal format 0x1e # hexadecimal 0X1E # hexadecimal 036 # octal, Python 2.6 0B11110 # binary 0b11110 # binary 0O36 # octal, Python 3.0 0o36 # octal, Python 3.0

If you try to represent an octal value in Python 3.0, as in Python 2.6 (036), the compiler will throw an error.

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##### 4. Types of integers in Python 2.6: regular and long. Example

In Python 2.6, integers can be represented by two types:

- regular (32-bit) numbers;
- long (unlimited precision) numbers. Such numbers end with the character
**l**or**L**. If the numeric value of an integer literal does not fit into a regular 32-bit number, then this value is automatically cast to a long integer. In this case, the interpreter automatically performs the corresponding conversion.

**Example.**

12345 # regular 32-bit number 1234567890l # long number in Python versions up to 3.0 7777777777777L # long number in Python versions up 3.0

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##### 5. Representation of integers in Python 3.0

In Python 3.0, both types of numbers (regular and long) were represented as a single (single) type of integers, which is automatically represented as a long integer (supports unlimited precision). Therefore, in this version of Python there is no need to complete literals with **l** or **L**. If you specify **l** or **L** after the number in Python 3.0, the interpreter will throw an “Invalid token” error.

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##### 6. Conversion functions of the numbers in the string, and vice versa hex(), oct(), bin(), int(). Examples

The following functions are used to turn the numeric form of a literal into a string:

- hex(num) – converts the number num to a string that displays this number in hexadecimal notation;
- oct(num) – converts the number num into a string that represents this number in octal;
- bin(num) – converts the number num to a string that represents this number in binary.

To convert a string to an integer taking into account the calculus system, use the function

`int(s, base)`

here

- s – a string;
- base – an integer that determines the number of digits in the number system. For example, for calculus 7, the value base = 7.

**Examples **of conversion functions.

sh = hex(15) # sa = 0xF so = oct(15) # sb = 0o17 sb = bin(15) # sb = 0b1111 i = int('15',10) # i = 15 i = int('15',8) # i = 13 # i = int('19',8) - error, the number 9 cannot be in the 8th calculus i = int('2EF',16) # i = 751 i = int('20',16) # i = 32 i = int('14',5) # i = 9

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##### 7. Representation of real numbers. Example

Real numbers define floating point numbers. Real numbers (literals) can be represented as:

- numbers that contain the separator of the integer and fractional part;
- numbers that contain the character
**e**or**E**to indicate the order of the number.

The Python interpreter recognizes a real number by the presence of the character **‘.’** (“dot”) or exponent (**e** or **E**). After the number is recognized, the corresponding object of a real type is created. Such an object is used in further mathematical expressions as an object of a real type (and not an object of an integer or another type).

**Example**.

2.85 # ordinary representation of a real number 3. # number 3.0 1.3e-3 # number 0.0013 1.52E6 # 1520000.0 3e2 # 300.0 2.0E-1 # 0.2

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**8. Complex numbers****. ****Examples**

Python has the ability to work with complex numbers. The general form for representing a complex number is as follows:

real_part+imag_partj

here

*real_part*– the real part of the complex number, which is optional (in the case when the number does not contain the real part);*imag_part*– the imaginary part of the complex number, which ends with the character**j**or**J**.

The interpreter represents a complex number as two real numbers. When used in mathematical expressions, complex numbers are processed accordingly.

**Examples** of complex number literals

6-8j 2.5+3.8j 0.001J 2.-3.J

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##### 9. Creating complex numbers. Function complex(). Example

Complex numbers are created by the complex() function, which is a built-in Python function. General form of function:

`complex(real, imag)`

**Example.**

a = complex(6, -8) # a = (6-8j) b = complex(0, 2.5) # b = 2.5j c = complex(0.02, -1e4) # c = (0.02-10000j)

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### Related topics

**Presentation of data**in Python. The concept of the**object**. Identity, type, value of the object. The functions**id()**,**type()**. Operators**is**,**is not****Literals.**Creation (generation) objects. Basic types of objects

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