Summary
This chapter explains Python’s floor division (`//`) and modulo (`%`) operations (including their behavior with negative operands), the built-in `round` function’s “round half to even” strategy, and how to use the `math` module for numeric tasks such as flooring, ceiling, truncating, square roots, constants (π, e), and finiteness checks.

General domain of usage
Time calculations (e.g., splitting seconds into hours and minutes)

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

Gain a solid understanding of Python's core data types and learn how to work with them effectively. Explore numbers, booleans, and strings through hands-on exercises and practical examples. Build confidence in performing basic operations and develop the foundational skills needed to write clean and efficient Python code.

Discover the essentials of numerical data types in Python and learn how to work with integers and floating-point numbers. Master basic arithmetic operations, explore the concept of immutability, and get hands-on experience using Python's built-in functions and tools to handle numbers efficiently in real-world scenarios.

Gain a clear understanding of the Boolean data type, a specialized subtype of numeric data that represents truth values. Although it may seem challenging at first, mastering Booleans is essential for writing logical and efficient programs. This section will help you confidently apply Boolean logic to real-world programming scenarios.

Strings allow you to work with text in Python, from displaying messages to processing user input. You'll explore how to create, modify, and manipulate strings effectively. Understanding strings is essential for writing interactive programs and communicating information clearly through your code.

Learn how to handle data types effectively to ensure accuracy and consistency in your programs. Convert values to the appropriate type, clean text before comparison, and separate numeric operations from text formatting. You'll also discover how to manage missing data deliberately and handle human-readable text differently from raw input, achieving reliable, consistent, and easy-to-read results.

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 %