Decimal Number System
Table of Content:
🔢 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:
- The digit itself
- Its position in the number
- 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:
| Number | Place Values |
|---|---|
| 145 | 1×10² + 4×10¹ + 5×10⁰ = 145 |
| 507 | 5×10² + 0×10¹ + 7×10⁰ = 507 |
| 8002 | 8×10³ + 0×10² + 0×10¹ + 2×10⁰ = 8002 |
🧩 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:
| Feature | Description |
|---|---|
| Base | 10 |
| Digits Used | 0 to 9 |
| Place Value System | Yes |
| Positional Power Rule | Each digit = d × 10^position |