Python Numbers and Arithmetic

Numbers are the workhorses of computation. Whether you're calculating grades, building simulations, or processing financial data, a solid grasp of Python's numeric types and operators is essential.

Python Numbers and Arithmetic

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Key Takeaways

• Python has two primary numeric types: int (whole numbers) and float (decimals)
• Seven arithmetic operators cover all common math operations
• Operator precedence follows standard math rules — use parentheses to be explicit
• Floating-point numbers have a well-known precision limitation you must account for
• Type conversion functions (int(), float(), str()) let you move between types safely

Integers and Floats

Python distinguishes between whole numbers and decimal numbers:

# Integers — whole numbers of arbitrary precision
population = 8_000_000_000    # underscores improve readability
negative = -42
zero = 0

# Floats — decimal (floating-point) numbers
temperature = 98.6
tiny = 0.001
scientific = 2.5e10           # 25,000,000,000.0

Python integers have no size limit — they grow as large as your memory allows. Floats, however, follow the IEEE 754 double-precision standard (64-bit).

🖼️ Visual Suggestion: A number line showing where integers and floats sit, highlighting that floats can represent values between integers.

Arithmetic Operators

Python provides seven arithmetic operators:

A key distinction: / always returns a float, even when dividing evenly (10 / 2 gives 5.0). Use // when you need an integer result.

# Division always returns a float
print(10 / 2)     # 5.0

# Floor division truncates the decimal
print(10 // 3)    # 3

# Modulo gives the remainder — useful for even/odd checks
print(10 % 2)     # 0 (even)
print(11 % 2)     # 1 (odd)

# Exponentiation replaces math.pow for simple cases
print(2 ** 10)    # 1024

Operator Precedence

Python follows the standard mathematical order of operations. From highest to lowest priority:

1. () — Parentheses (always evaluated first)
2. ** — Exponentiation
3. *, /, //, % — Multiplication, division, floor division, modulo
4. +, - — Addition and subtraction

# Without parentheses — multiplication happens first
result = 2 + 3 * 4
print(result)  # 14, not 20

# Parentheses override the default order
result = (2 + 3) * 4
print(result)  # 20

Best practice: even when you know the precedence rules, use parentheses to make your intent explicit. Your future self will thank you.

The Float Precision Gotcha

This trips up every Python beginner at some point:

print(0.1 + 0.2)  # 0.30000000000000004 — not 0.3!

This isn't a Python bug — it's a fundamental limitation of binary floating-point representation. The number 0.1 cannot be represented exactly in binary, just like 1/3 can't be written exactly in decimal.

How to Handle It

# Option 1: Round the result
print(round(0.1 + 0.2, 1))  # 0.3

# Option 2: Use the decimal module for precise arithmetic
from decimal import Decimal
print(Decimal("0.1") + Decimal("0.2"))  # 0.3 — exact

# Option 3: Compare with a tolerance instead of strict equality
import math
print(math.isclose(0.1 + 0.2, 0.3))  # True

🖼️ Visual Suggestion: A callout box highlighting that financial calculations should always use the decimal module, never raw floats.

Mixing Strings and Numbers: TypeError

Python refuses to silently coerce types. Trying to concatenate a string and a number raises a TypeError:

age = 25

# This raises TypeError: can only concatenate str (not "int") to str
# print("I am " + age + " years old.")

# Fix: convert the number to a string explicitly
print("I am " + str(age) + " years old.")

# Better: use an f-string (no manual conversion needed)
print(f"I am {age} years old.")

Type Conversion Functions

Python provides built-in functions to convert between types:

# String to integer
user_input = "42"
number = int(user_input)
print(number + 8)    # 50

# String to float
price = float("19.99")
print(price * 2)     # 39.98

# Number to string
score = 100
message = "Your score: " + str(score)
print(message)       # "Your score: 100"

# Float to integer (truncates — does NOT round)
print(int(3.9))      # 3
print(int(-3.9))     # -3

Caution: int() truncates toward zero, it does not round. If you need rounding, use round() first.

Putting It All Together

# A small tip calculator
bill = 85.50
tip_rate = 0.18
party_size = 4

tip = bill * tip_rate
total = bill + tip
per_person = round(total / party_size, 2)

print(f"Bill: ${bill}")
print(f"Tip ({tip_rate:.0%}): ${tip:.2f}")
print(f"Total: ${total:.2f}")
print(f"Per person: ${per_person}")

Up next: we'll explore conditional logic with if/elif/else — the decision-making engine of every Python program.