# Numbers and arithmetics¶

Now let’s have a look at some objects in Python which are used to represent numbers.

## Integers and decimal numbers¶

The two main ones are: `int`

(integers) and `float`

(decimal numbers):

```
>>> # this is an integer
>>> A = 12
>>> type(A)
<type 'int'>
>>> # this is a float
>>> B = 12.5
>>> type(B)
<type 'float'>
```

The only difference in terms of notation if the use of a period for decimal numbers. A number is a decimal number even if there is no digit after the period:

```
>>> # this is still a float
>>> C = 12.
>>> type(C)
<type 'float'>
```

## Arithmetic Operations¶

### Addition¶

Adding numbers is easy and intuitive: simply use the `+`

operator

```
>>> 1 + 1
2
>>> 1 + 1 + 10
12
```

Integers can be added to integers, floats can be added to floats, and integers can be added to floats (and vice-versa):

```
>>> # result is an integer
>>> 12 + 13
25
>>> # result is a float
>>> 12 + 0.5
12.5
>>> # result is a float
>>> 0.5 + 12.5
13.0
```

If both numbers are integers, the result is also an integer. If at least one of the numbers is a float, the result will be a float.

### Subtraction¶

Subtracting numbers follows the same logic, just use the `-`

operator:

```
>>> 12 - 8
4
```

The minus sign is also used to indicate negative numbers:

```
>>> 12 - 25
-13
```

### Multiplication¶

In Python, the multiplication operator is the `*`

character, rather than `×`

(multiplication sign) as usual in maths. But it works exactly the same way:

```
>>> 12 * 8
96
>>> 12 * -25
-300
```

### Division¶

Division in Python uses the `/`

(forward slash) as its operator:

```
>>> 11 / 2
5
```

Warning

The default division behavior in Python 2.x is *floor division* — the result is rounded down to the nearest integer. This is usually weird for beginners.

In Python 2.x, if you need the division result as a float, you’ll need to convert one of the numbers to float first:

```
>>> 11 / 2.
5.5
```

In Python 3, the division operator uses float division as its default. As with other Python 3 features, it is possible to use float division as default in Python 2.x by importing it from the `__future__`

module:

```
>>> 11 / 2
5
>>> from __future__ import division
>>> 11 / 2
5.5
```

Division by zero is mathematically not possible and will always raise an error:

```
>>> 1 / 0
Traceback (most recent call last):
File "<untitled>", line 1, in <module>
ZeroDivisionError: integer division or modulo by zero
```

Integer division can be performed with the special operator `//`

:

```
>>> 11 // 2
5
```

Finally, use the `%`

operator to get the rest of a division (modulo):

```
>>> 11 % 2
1
```

### Exponentiation¶

To elevate a number to the power of another number, the operator `**`

is used:

```
print 2 ** 8
print 10 ** 2
print 2 ** 0.5
```

### Combining operations¶

Arithmetic operations can be combined into larger statements and calculations:

```
print 7 + 10 - 100 * 3 / 200 ** 4
```

Python executes division and multiplication first, and addition and subtraction afterwards. If you want to add or subtract first, you must put these operations between parentheses – Python will execute operations between parentheses first:

```
>>> 9 * 9 + 2
83
>>> 9 * (9 + 2)
99
```

### Increment/decrement operators¶

Sometimes when writing code it is necessary to increment or decrement a value (to add or subtract a value from an integer):

```
a = 10
a = a + 2
```

In cases like this, it possible to write the same line using the increment `+=`

operator:

```
# a = a + 2
a += 2
```

...and a decrement operator `-=`

is also available:

```
# b = b - 1
b -= 1
```

There is also an incrementing product operator `*=`

:

```
# c = c * 10
c *= 10
```

## More math¶

Python can do many other kinds of mathematical calculations, of course. Many of these mathematical functions live in the math module. For example, trigonometric functions such as *sine*, *cosine*, *tangent*; constants such as *pi*, etc.

```
>>> import math
>>> print math.pi
3.14159265359
```