Summary  
This chapter explains floor division, modulo arithmetic (including behavior with negative operands), Python’s “round half to even” rounding rule, and key numeric functions/constants in the math module (e.g., floor, ceil, trunc, sqrt, π, e, isfinite, isnan, isinf).

General domain of usage  
Time calculations (e.g., converting total seconds into hours and minutes or handling clock arithmetic)

Learn how Python handles **floor division** and **modulo** (including negative numbers) and explore the **`math`** module for common numeric operations.


## Floor Division (`//`)

Returns the **floor** of the exact quotient, meaning it **rounds the result down**.


print(7 // 3)    # 2
print(-7 // 3)   # -3   (floors down: -2.333... → -3)

**Why it matters:** indexing chunks/pages, time splitting (hours from seconds), and any "how many full groups fit" calculation.

## Modulo `%`

Returns the **remainder** of division.
In Python, the remainder always has the **same sign as the divisor**.



print(7 % 3)    # 1
print(-7 % 3)   # 2
print(7 % -3)   # -2

**Why it matters:** "every Nth" item, wrap-around (e.g., clock arithmetic), cycling through buckets.

**Examples:**

* Keeping track of **hours on a clock** → `14 % 12 = 2` - (2 PM);
* Selecting **every 3rd item** in a list → `if i % 3 == 0:`.

## Quick Note on Rounding

Built-in `round(x, ndigits)` uses **"round half to even"**.

print(round(2.5), round(3.5))   # 2  4
print(round(2.675, 2))          # 2.67  (binary float nuance)

## The `math` Module

Import once and access many handy functions/constants.

import math

print(math.floor(2.9), math.ceil(2.1), math.trunc(-2.9))  # 2  3  -2
print(math.sqrt(9))                                       # 3.0
print(math.pi, math.e)                                    # 3.14159...  2.71828...
print(math.isfinite(1.0), math.isfinite(float('inf')))    # True False

A focused, beginner-friendly course on working with numbers in Python. Learn about integers, floats, arithmetic operations, type conversion, and how to avoid common pitfalls when handling numerical data.

Advanced Arithmetic

Floor Division (`//`)

Modulo `%`

Quick Note on Rounding

The `math` Module

1. What value will this code output?

2. What value will this code output?

3. Which call returns `-3`?

Advanced Arithmetic

Floor Division (//)

Modulo %