Base-10 (Decimal) Number System

Understanding the decimal number system - the foundation of everyday mathematics and the gateway to understanding other number systems in computing.

The base-10 number system, also known as the decimal system, uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

This system likely originated from humans having 10 fingers, making it natural for counting
It's the most commonly used number system in everyday life
Forms the foundation for understanding other number systems used in computing
Each position represents a power of 10

Each position in a decimal number represents a power of 10:

Position	Power of 10	Value	Example Digit	Contribution
Thousands	10³	1000	2	2 × 1000 = 2000
Hundreds	10²	100	5	5 × 100 = 500
Tens	10¹	10	3	3 × 10 = 30
Units	10⁰	1	7	7 × 1 = 7

Example: The number 2537 = (2×1000) + (5×100) + (3×10) + (7×1) = 2000 + 500 + 30 + 7

Understanding base-10 is crucial in computing because:

Application	Example	Range/Format	Description
File Sizes	1,024 bytes = 1 KB	0 to ∞	Storage capacity measurement
IP Addresses	192.168.1.1	0-255 per octet	Network device identification
RGB Colors	Red(255), Green(128), Blue(64)	0-255 per channel	Color representation
Port Numbers	HTTP(80), HTTPS(443)	0-65535	Network service identification

Break down numbers into their place value components:

Example: 4729 = (4×1000) + (7×100) + (2×10) + (9×1)

Practice: Break down 8456

Solution: 8456 = (8×1000) + (4×100) + (5×10) + (6×1)

= 8000 + 400 + 50 + 6

Practice operations using place value understanding:

Calculate: 250 + 340

Solution:

250 + 340

= (2×100 + 5×10) + (3×100 + 4×10)

= (2+3)×100 + (5+4)×10

= 5×100 + 9×10 = 590