Python’s real number (float) type

Python uses float to represent real numbers such as 1.5, 3.14, or 2.7. The name float came from the fact that real numbers are represented in the floating point format in computers.

For example: 3.14 can be represented as 3.14, 0.314 * 10^1, or 31.4 * 10^(-1). However, you can safely ignore this technical detail and think of a float just as a real number.

Create a float

We can create a float variable through an assignment with a real number literal, for example

x = 1.5
print(x)
print(type(x))
1.5
<class 'float'>

Note that 5.0 and 5 are of different types

type(5)
int
type(5.0)
float

Although they are equal in value

5 == 5.0
True

Also, 5., 5.0, and 5.000 are all the same

print(5.)
print(5.0)
print(5.000)
5.0
5.0
5.0

Similarly, 0.5 and .5 are the same

print(0.5)
print(.5)
0.5
0.5

We can also create a float variable through an assignment with an expression that produces a float, for example

1.5 + 3.7
5.2
2 / 3
0.6666666666666666

Another way to create a float is to use scientific notation

# One thousand
1e3
1000.0
# Ten million
10e6
10000000.0
# 1.23 billion
1.23e9
1230000000.0

When use float?

For storing real numbers in general. In many applications, we often treat 5.0 (float) and 5 (int) as if they are the same.

Typecasting

We use float() function to convert values from other types to float. However, not all values can be converted to float (only float-like values can).

Example 1: values that can be converted to float

From bool

# True becomes 1.0
float(True)
1.0
# False becomes 0.0
float(False)
0.0

From int

# Just change the type
float(12)
12.0

From str

# Strings that look like a float
x = float("10.5")
print(x)
print(type(x))
10.5
<class 'float'>
# White spaces at two ends are ignored
x = float("  -10.5 ")
print(x)
print(type(x))
-10.5
<class 'float'>
# Leading zeros are also ignored
x = float("  -00010 ")
print(x)
print(type(x))
-10.0
<class 'float'>

Operations on float

Arithmetic operations

Same as with integers. However, we cannot perform // and % on float values, because they are only mathematically meaningful for integers.

Here are some simple examples

# Float plus float yields float
1.5 + 3.7
5.2
# Int plus float yields float
# result is promoted to a more general type
5 + 1.0
6.0
# Compute square root
# by raising to power 0.5
25**(0.5)
5.0
# Rounding
round(10 / 3, 3)
3.333
# Get absolute values
print(abs(10.5))
print(abs(-10.5))
10.5
10.5

Comparision operations

Comparisons on numbers (int or float) always return a bool. (Already covered in the previous chapter)

Math utilities

Note: this section applies to numbers, thus to both int and float.

The Python standard libraries come with a module named math containing utilities for dealing with numbers. You will learn more about modules later. For now, just follow some simple examples.

To use math module, we need to import it. Then use the syntax math.<name_of_function> to call the function we want to use.

# Import module math
import math

Ceiling function — round UP to the nearest integer.
(if you are not sure, get help using ? such as ?math.ceil)

# With positive value
math.ceil(3.333)
4
# With negative value
math.ceil(-3.333)
-3

Floor function — round DOWN to the nearest integer.

# With positive value
math.floor(3.333)
3
# With negative value
math.floor(-3.333)
-4

math also provides useful constants, for example

# Constant pi
math.pi
3.141592653589793
# Constant e
math.e
2.718281828459045

Trigonometry functions

# Sin pi/2 => 1
math.sin(math.pi / 2)
1.0
# Cos pi / 2 => 0
# Note that the result is not 0
# but very close (due to approximation error)
math.cos(math.pi / 2)
6.123233995736766e-17

For the full list of what you can do with math, visit its official documentation page at https://docs.python.org/3/library/math.html

However, strings like "1,000,000.123" (contains ,) are not valid. Try it yourself to see the error.

Practice

Ex 1

Do the following

• Create float variable x with value 100
• Show its value and type

Ex 2

Do the following

• Create a variable x from the division of 10 by 5
• Show the value and type of x

Ex 3

How to quickly create a value of 7.5 billion?

Ex 4

Use math module to compute

• The area of a circle with a radius 5
• The hypotenuse of a right triangle with 3 and 4 being the lengths of the two other sides

Navigation

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