🔸 Real Numbers & Floating Point

📖 What Is a Real Number?

A real number (also called a float or floating-point number) is any number that can have a decimal point. It includes whole numbers written with a decimal (like 5.0) and fractional values (like 3.14).

Valid floats: 3.14, -0.5, 99.99, 0.0, 2.0

💡 What Is "Single Precision Floating Point"?

Computers store decimals using a system called floating point. There are two levels of accuracy:

Type	Bits	Decimal Accuracy	Use Case
Single precision	32 bits	~7 digits	Games, graphics, GPS — where speed matters more than perfect accuracy
Double precision	64 bits	~15 digits	Science, finance — where accuracy is critical

Single precision uses less memory and is faster, which is why game engines like Unity and Unreal use it for positions, rotations, and physics. The trade-off: it can have tiny rounding errors after ~7 decimal digits.

🎮 Where Floats Are Used in Games

Game	Float Data	Example Value
Fortnite	Player position (x, y, z), weapon accuracy	x = 1547.832, accuracy = 0.85
Minecraft	Player speed, exact position	speed = 4.317, y = 63.5
Any game	Volume level, brightness, sensitivity	volume = 0.75, brightness = 1.2

🐍 Floats in Python

🐍 Floats — decimal numbers

# Floats have decimal points
player_x = 1547.832
accuracy = 0.85
price = 19.99

print("Position:", player_x, "| Type:", type(player_x))
print("Accuracy:", accuracy, "| Type:", type(accuracy))
print("Price:", price, "| Type:", type(price))

# Float maths
discount = price * 0.25
print()
print("25% discount on $" + str(price) + ": -$" + str(discount))
print("You pay: $" + str(price - discount))

# The famous floating point quirk!
print()
print("0.1 + 0.2 =", 0.1 + 0.2)
print("(Not exactly 0.3! This is a floating point rounding issue)")

💡 The Famous 0.1 + 0.2 Problem

Run the code above and look at the last line. 0.1 + 0.2 gives 0.30000000000000004 — not exactly 0.3! This is because decimal fractions like 0.1 cannot be represented perfectly in binary floating point. It is a tiny rounding error that exists in every programming language. This is why money calculations often use integers (cents) instead of floats.