Numbers

Beginner ~25 min read

Python supports three numeric types: integers (whole numbers), floats (decimal numbers), and complex numbers. This lesson covers each type, arithmetic operations, and the powerful math module.

Integers (int)

Integers are whole numbers without decimal points. Unlike many languages, Python integers have unlimited precision - they can be as large as your memory allows!

Output

Click Run to execute your code

Number Bases: Python supports binary (0b), octal (0o), and hexadecimal (0x) notation. This is useful when working with low-level data, colors (hex), or file permissions (octal).

Floating Point Numbers (float)

Floats represent decimal numbers. They use the IEEE 754 double-precision format, giving about 15-17 digits of precision.

Output

Click Run to execute your code

Float Precision: 0.1 + 0.2 doesn't equal 0.3 exactly! This is a fundamental limitation of binary floating-point representation. For financial calculations, use the decimal module.

Complex Numbers (complex)

Complex numbers have a real and imaginary part. Python uses j for the imaginary unit (mathematicians use i, engineers use j).

Output

Click Run to execute your code

When to use complex: Complex numbers are essential in electrical engineering, signal processing, quantum computing, and certain mathematical algorithms.

Arithmetic Operations

Python provides all standard arithmetic operators:

Operator	Name	Example	Result
`+`	Addition	`5 + 3`	8
`-`	Subtraction	`5 - 3`	2
`*`	Multiplication	`5 * 3`	15
`/`	Division	`5 / 3`	1.666...
`//`	Floor Division	`5 // 3`	1
`%`	Modulo	`5 % 3`	2
`**`	Exponent	`5 ** 3`	125

# Arithmetic Operations in Python

a = 17
b = 5

print(f"a = {a}, b = {b}")
print("-" * 30)

# Basic operations
print(f"Addition:       a + b = {a + b}")
print(f"Subtraction:    a - b = {a - b}")
print(f"Multiplication: a * b = {a * b}")
print(f"Division:       a / b = {a / b}")      # Always returns float

# Integer division and modulo
print(f"\nInteger division: a // b = {a // b}")  # Floor division
print(f"Modulo (remainder): a % b = {a % b}")

# Power
print(f"\nPower: a ** b = {a ** b}")             # 17^5
print(f"Also: pow(a, b) = {pow(a, b)}")

# divmod - returns both quotient and remainder
quotient, remainder = divmod(a, b)
print(f"\ndivmod({a}, {b}) = ({quotient}, {remainder})")
print(f"Verification: {quotient} * {b} + {remainder} = {quotient * b + remainder}")

# Negative number division
print(f"\nNegative division:")
print(f"-17 // 5 = {-17 // 5}")   # Rounds toward negative infinity
print(f"-17 % 5 = {-17 % 5}")     # Result has same sign as divisor

# Operator precedence (PEMDAS)
print(f"\nPrecedence example:")
print(f"2 + 3 * 4 = {2 + 3 * 4}")       # 14, not 20
print(f"(2 + 3) * 4 = {(2 + 3) * 4}")   # 20

Output

Click Run to execute your code

Division Note: In Python 3, / always returns a float. Use // for integer (floor) division. In Python 2, / performed integer division if both operands were integers.

The Math Module

Python's math module provides advanced mathematical functions:

# Math Module in Python
import math

print("Math Constants:")
print(f"pi = {math.pi}")
print(f"e = {math.e}")
print(f"tau (2*pi) = {math.tau}")
print(f"inf = {math.inf}")

print("\n" + "=" * 40)
print("Rounding Functions:")
x = 3.7
print(f"x = {x}")
print(f"floor(x) = {math.floor(x)}")    # Round down: 3
print(f"ceil(x) = {math.ceil(x)}")      # Round up: 4
print(f"trunc(x) = {math.trunc(x)}")    # Truncate: 3
print(f"round(x) = {round(x)}")         # Built-in round: 4

print("\n" + "=" * 40)
print("Power & Logarithms:")
print(f"sqrt(16) = {math.sqrt(16)}")
print(f"pow(2, 10) = {math.pow(2, 10)}")
print(f"log(100) = {math.log(100):.4f}")       # Natural log
print(f"log10(100) = {math.log10(100)}")       # Base 10
print(f"log2(256) = {math.log2(256)}")         # Base 2

print("\n" + "=" * 40)
print("Trigonometry (radians):")
angle = math.pi / 4  # 45 degrees
print(f"sin(45°) = {math.sin(angle):.4f}")
print(f"cos(45°) = {math.cos(angle):.4f}")
print(f"tan(45°) = {math.tan(angle):.4f}")

print("\n" + "=" * 40)
print("Other useful functions:")
print(f"abs(-5) = {abs(-5)}")
print(f"factorial(5) = {math.factorial(5)}")
print(f"gcd(48, 18) = {math.gcd(48, 18)}")
print(f"isnan(float('nan')) = {math.isnan(float('nan'))}")

Output

Click Run to execute your code

Common Mistakes

1. Integer division expecting float result

# Oops - using // when / was intended
result = 7 // 2    # Returns 3, not 3.5
result = 7 / 2     # Returns 3.5

2. Comparing floats for equality

# Don't do this
if 0.1 + 0.2 == 0.3:  # False!

# Do this instead
if abs((0.1 + 0.2) - 0.3) < 0.0001:  # True

3. Division by zero

# This raises ZeroDivisionError
result = 10 / 0

# Check first
if divisor != 0:
    result = 10 / divisor

Exercise: Simple Calculator

Task: Given two numbers, perform all arithmetic operations and display the results.

Requirements:

Calculate: addition, subtraction, multiplication
Calculate: division (both regular and integer)
Calculate: modulo and power (num1 squared)

Output

Click Run to execute your code

Show Solution

num1 = 25
num2 = 7

print(f"{num1} + {num2} = {num1 + num2}")
print(f"{num1} - {num2} = {num1 - num2}")
print(f"{num1} * {num2} = {num1 * num2}")
print(f"{num1} / {num2} = {num1 / num2:.3f}")
print(f"{num1} // {num2} = {num1 // num2}")
print(f"{num1} % {num2} = {num1 % num2}")
print(f"{num1} ** 2 = {num1 ** 2}")

Summary

int: Whole numbers with unlimited precision
float: Decimal numbers (IEEE 754 double-precision)
complex: Numbers with real and imaginary parts (3+4j)
Division: / returns float, // returns integer
Math module: Use import math for advanced functions
Precision: Use decimal module for financial calculations

What's Next?

In the next lesson, we'll explore strings - Python's powerful text data type, including indexing, slicing, and common string operations.

Previous Variables

Next Strings

Integers (int)

Floating Point Numbers (float)

Complex Numbers (complex)

Arithmetic Operations

The Math Module

Common Mistakes

1. Integer division expecting float result

2. Comparing floats for equality

3. Division by zero

Exercise: Simple Calculator

Summary

What's Next?

Enjoying these tutorials?