77 exercises

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()`

`bin()`

`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'>
```

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 operators behave as they do in normal math.
If one or more of the operands is a `float`

, the remaining `int`

s will be converted to `float`

s as well:

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

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 always returns a `float`

, even if the result is a whole number:

```
>>> 6/5
1.2
>>> 6/2
3.0
```

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
```

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 is performed using the `**`

operator:

```
>>> 2 ** 3
8
>>> 4 ** 0.5
2
```

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
```

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
```

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
```

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.