Python - Floating Point

Floats are a built-in numeric data type in Python used to represent real numbers that contain a decimal part. Any real number that has a decimal point is classified as a floating-point number in Python, even if the decimal part is zero (0), e.g., 6.0.

How to Represent a Float

A float can be initialized by adding a decimal point to any number; in fact, a number is classified as a float in Python the moment it contains a decimal point.

# A standard floating point number
pi = 3.14159

# Even if the fractional part is zero, the decimal makes it a float
x = 10.0

Leading and Trailing Decimals

Python allows for shorthand notation where the leading or trailing zero can be omitted.

• .5 is interpreted as 0.5
• 5. is interpreted as 5.0

Using Scientific Notation in Floats

To represent very large or very small numbers, Python provides the scientific notation e or E. This notation multiplies a number by a power of 10. For those familiar with mathematics, the value after e represents the exponent of 10. For example, 1e3 means 1 × 10³.

Mathematical Representation:
A number $n$ in scientific notation $ae^b$ is defined as:

# 1.5 times 10 to the power of 2 (150.0)
large_val = 1.5e2

# 3 times 10 to the power of -2 (0.03)
small_val = 3e-2

Technical Limitations of Floats:

Because numbers are represented in base-2 rather than base-10, some fractions cannot be stored exactly. This introduces small precision errors that are usually insignificant in calculations, but can cause unexpected results in logical comparisons.

The widely know 0.1 + 0.2 Problem:

a = 0.1
b = 0.2

result = a + b

print(f"{result:.17f}") # Output: 0.30000000000000004
print(result == 0.3)    # False

Due to this binary approximation, floating point numbers should generally not be compared for exact equality (==) in financial or high-precision calculations.

The float() Constructor

We use the float() constructor to convert intergers or compactible strings to floating point numbers

# Converting an integer to a float
y = float(10)  # Result: 10.0

# Converting a string to a float
z = float("3.5") # Result: 3.5

The .is_integer() Method

Floats have a built-in method called .is_integer() which returns True if the float has no fractional part (i.e., it is a whole number).

val1 = 10.0
print(val1.is_integer()) # Output: True

val2 = 10.5
print(val2.is_integer()) # Output: False

Do not confuse this with isinstance(). The .is_integer() method checks whether a float's value is mathematically a whole number, while isinstance() checks the object's type. Even if 3.0.is_integer() returns True, isinstance(3.0, float) will still return True because the object remains a float.

number = 3.0

print(number.is_integer())          # True
print(isinstance(number, float))    # True

number = 3.5

print(number.is_integer())          # False
print(isinstance(number, float))    # True

In the first example, 3.0 is stored as a float, but it has no fractional part, so .is_integer() returns True. However, isinstance() still reports that the object is a float.

Summary

• Definition: Floats are numbers with decimal points used for fractional precision.
• Scientific Notation: Supported via e or E for powers of 10 ($a \times 10^b$).
• Comparison: Avoid using == for floats due to precision ghosts.
• Verification: Use .is_integer() to check if a float represents a whole number.