What are Floating Point Numbers in Python?

In this tutorial, I will explain what are floating point numbers in Python. Someone asked me this question in a Python webinar and I decided to write an article on this topic. I will share my findings in this tutorial with examples and screenshots of executed example code.

Table of Contents:

Floating Point Number in Python

A floating point number is a number with a decimal point or exponent notation, indicating that a number has a fractional component. For example, numbers like 3.14, 98.6, and -0.001 are all floating point numbers in Python.

Internally, floating-point numbers are represented in computer hardware as base 2 (binary) fractions. While this allows for efficient storage and calculations, it can sometimes lead to precision limitations and rounding errors, which we’ll discuss later.

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Create Floating Point Numbers

In Python, you can create a floating point number simply by including a decimal point in a numeric literal:

pi = 3.14159
body_temp = 98.6

You can also use scientific notation with the letter ‘e’ to represent powers of 10:

avogadro_number = 6.022e23
electron_charge = -1.602e-19

Python also provides a built-in float() function that can convert integers, strings, or other number types into floating point numbers:

float_value = float(42)    # 42.0
string_float = float("3.14")    # 3.14

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Floating Point Arithmetic

Python supports standard arithmetic operations on floating point numbers, such as addition, subtraction, multiplication, and division:

california_sales_tax = 0.0725
item_price = 9.99

total_price = item_price * (1 + california_sales_tax)
print(f"Total price in California: ${total_price:.2f}")

Output:

Total price in California: $10.71

I executed the above example code and added the screenshot below.

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Precision and Rounding Errors

Due to the way floating point numbers are represented in binary, some decimal fractions cannot be represented exactly, leading to small rounding errors. For example:

result = 0.1 + 0.2
print(result)

Output:

0.30000000000000004

I executed the above example code and added the screenshot below.

What are Floating Point Numbers in Python

In most cases, these small discrepancies won’t cause issues, but it’s important to be aware of them, especially when comparing floating point numbers for equality.

If you need exact decimal representation, you can use the built-in decimal module, which provides support for fast correctly-rounded decimal floating point arithmetic.

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Floating Point Methods

The float type in Python provides several useful methods for working with floating point numbers:

is_integer(): Returns True if the float instance is finite with integral value, and False otherwise.

value = 3.0
print(value.is_integer()) 

value = 3.14
print(value.is_integer())

Output:

True
False

I executed the above example code and added the screenshot below.

Floating Point Numbers in Python Floating Point Methods

hex(): Returns a string representation of the float in hexadecimal format.

value = 42.0
print(value.hex())

Output:

as_integer_ratio(): Returns a pair of integers whose ratio is exactly equal to the original float and with a positive denominator.

value = 3.14
print(value.as_integer_ratio())

Output:

(157, 50)

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Conclusion

In this tutorial, I have explained what are floating point numbers in Python. I discussed how to create floating point numbers, floating point algorithmic, precision and rounding errors, and floating point methods.