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The float type in Python is a built-in numeric data type used to represent real numbers with a fractional component. In CPython, a float is implemented as a C double, meaning it strictly adheres to the IEEE 754 double-precision binary floating-point standard. It occupies 64 bits of memory: 1 bit for the sign, 11 bits for the exponent, and 52 bits for the significand (mantissa).

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Instantiation and Syntax

Floats can be instantiated using numeric literals containing a decimal point, scientific notation (E-notation), or the built-in float() constructor. 

# Decimal literals
val_standard = 3.14159
val_leading  = .5      # Evaluates to 0.5
val_trailing = 4.      # Evaluates to 4.0


# Scientific notation (E-notation)
val_large = 1.5e5      # Evaluates to 150000.0
val_small = 2.5e-3     # Evaluates to 0.0025


# Constructor casting
from_int = float(42)       # Evaluates to 42.0
from_str = float("-3.14")  # Evaluates to -3.14

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Special Values

The float type supports special IEEE 754 values representing infinity and undefined mathematical operations (Not a Number). These are typically instantiated via string casting. 
pos_inf = float('inf')   # Positive infinity
neg_inf = float('-inf')  # Negative infinity
nan_val = float('nan')   # Not a Number


# NaN identity quirk: NaN is never equal to itself
print(nan_val == nan_val)  # False

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Precision and Limits

Because Python floats are 64-bit double-precision values, they are subject to strict hardware limitations regarding maximum value and precision. These system-level constraints can be inspected using the sys module. 
import sys


# Maximum representable finite float
print(sys.float_info.max)      # ~1.7976931348623157e+308


# Minimum representable positive normalized float
print(sys.float_info.min)      # ~2.2250738585072014e-308


# Difference between 1.0 and the least value greater than 1.0
print(sys.float_info.epsilon)  # ~2.220446049250313e-16

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Representation Error

Because floats are stored as base-2 (binary) fractions, most base-10 (decimal) fractions cannot be represented exactly. This results in representation error, where the stored value is a highly precise approximation. 

# Binary approximation of 0.1 and 0.2 leads to a floating-point artifact
result = 0.1 + 0.2
print(result)          # 0.30000000000000004
print(result == 0.3)   # False


# Standard technical resolution for equality checks
import math
print(math.isclose(0.1 + 0.2, 0.3))  # True

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Type Methods

The float object includes several built-in methods for mathematical introspection and conversion. 
f = 3.125


# Returns a tuple of (numerator, denominator) in lowest terms
print(f.as_integer_ratio())  # (25, 8)


# Checks if the float has no fractional part
print(f.is_integer())        # False
print(3.0.is_integer())      # True


# Returns the exact hexadecimal string representation of the float
print(f.hex())               # '0x1.9000000000000p+1'
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