Python Numbers

Python Numbers: int, float, & complex Operations

Python provides three distinct numerical types: arbitrary-precision integers (int), double-precision floating-point numbers (float), and complex numbers (complex).

Numeric Types Architecture

flowchart LR
    A["Numeric Input"] --> B{"Contains decimal/e?"}
    B -- "No" --> C["int (Arbitrary Precision)"]
    B -- "Yes" --> D{"Contains 'j'?"}
    D -- "No" --> E["float (IEEE 754 Double)"]
    D -- "Yes" --> F["complex (real + imag j)"]

Numeric Types & Limits

• int: Unlimited precision integer; expands dynamically in memory as needed without integer overflow bugs.
• float: Implemented using C double (64-bit IEEE 754 floating-point standard).
• complex: Stored as two 64-bit floats (real + imag * 1j).

Practical Code Example

import math
from decimal import Decimal, getcontext

def numeric_operations_demo() -> None:
    # Large integer handling
    large_int: int = 10 ** 30
    print(f"2^30 power integer: {large_int}")

    # Float precision limitation vs Decimal solution
    float_sum: float = 0.1 + 0.2
    print(f"Standard float 0.1 + 0.2: {float_sum:.17f}")  # 0.30000000000000004
    
    # Financial precision with Decimal module
    getcontext().prec = 6
    dec1 = Decimal("0.1")
    dec2 = Decimal("0.2")
    print(f"Decimal 0.1 + 0.2: {dec1 + dec2}")  # 0.3 Exact

    # Complex number math
    c1: complex = 3 + 4j
    print(f"Complex Number: {c1}, Magnitude (abs): {abs(c1)}")

if __name__ == "__main__":
    numeric_operations_demo()

Best Practices & Gotchas

• Use Decimal for Financial Calculations: Standard float arithmetic introduces precision errors (0.1 + 0.2 != 0.3). Use decimal.Decimal for currency values.
• Floor Division (//) vs True Division (/): / always returns a float, whereas // returns the integer quotient.
• Use math.isclose(): Never compare float values directly with ==; use math.isclose(a, b, rel_tol=1e-9).

Self-Check Challenge

Write a script that accepts a price as a string "19.99" and tax rate "0.07", computes the total using decimal.Decimal, and prints the result rounded to 2 decimal places.