Decimal Number System

🔢 Decimal Number System

📘 Introduction

The Decimal Number System is the most commonly used number system in our everyday life. It is also known as the Base-10 number system because it uses 10 unique digits.

🔟 Digits Used:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Each digit in a number has a place value depending on its position and is a power of 10.

🧠 Positional Value Concept

In the positional number system, the value of each digit depends on:

1. The digit itself
2. Its position in the number
3. The base of the number system

📌 General Formula:

If a number has digits dₙ dₙ₋₁ ... d₂ d₁ d₀, then:

Value of the number =
dₙ × 10ⁿ + dₙ₋₁ × 10ⁿ⁻¹ + ... + d₂ × 10² + d₁ × 10¹ + d₀ × 10⁰

✅ Examples:

Example 1:

(99)₁₀
= 9 × 10¹ + 9 × 10⁰
= 90 + 9
= 99

Example 2:

(332)₁₀
= 3 × 10² + 3 × 10¹ + 2 × 10⁰
= 300 + 30 + 2
= 332

Example 3:

(1024)₁₀
= 1 × 10³ + 0 × 10² + 2 × 10¹ + 4 × 10⁰
= 1000 + 0 + 20 + 4
= 1024

🔄 Counting in Decimal:

🧩 Why Decimal?

• Easy for humans to use (we have 10 fingers!)

• Used in all financial, scientific, and daily life calculations

• The base-10 system forms the foundation of all higher-level arithmetic

✅ Summary: