Babylonian Calculator (Base-60)
Convert decimal numbers to the ancient Babylonian sexagesimal (base-60) system and vice versa.
Number Conversion
The Babylonian Number System
The Babylonians, who lived in Mesopotamia (modern-day Iraq) from around 3000 BC to 539 BC, developed a sophisticated sexagesimal (base-60) numeral system. This system was positional, meaning the value of a digit depended on its position, much like our modern decimal system.
Key Features:
- Base-60: Numbers were grouped in powers of 60.
- Cuneiform Symbols: They used two basic wedge-shaped cuneiform symbols: a vertical wedge ( resembling 'Y' ) for units (1) and a horizontal wedge ( resembling '<' ) for tens (10).
- Positional Notation: The position of a symbol indicated its place value (e.g., 60^0, 60^1, 60^2, etc.).
- No Zero Placeholder (initially): Early Babylonian texts lacked a symbol for zero, which could lead to ambiguity. A placeholder symbol emerged later.
Babylonian Number Examples
| Decimal | Babylonian (Base-60) | Explanation |
|---|---|---|
| 1 |  | One unit |
| 10 |  | One ten |
| 59 |  | Five tens and nine units |
| 60 | ,  | One sixty, zero units (1,0) |
| 65 | ,  | One sixty, five units (1,5) |
| 3600 | , , | One (60^2), zero (60^1), zero (60^0) (1,0,0) |
Frequently Asked Questions
What was the Babylonian number system?
The ancient Babylonians used a sexagesimal (base-60) number system, which was positional, similar to our modern decimal system but with a base of 60 instead of 10. This system influenced our modern measurement of time (60 seconds in a minute, 60 minutes in an hour) and angles (360 degrees in a circle).
How did Babylonians write numbers?
Babylonian numbers were written using cuneiform script on clay tablets. They primarily used two symbols: a vertical wedge for units (1) and a horizontal wedge for tens (10). These symbols were combined to represent numbers within each base-60 place value.
Why did Babylonians use base-60?
The exact reasons are debated, but base-60 is highly composite, meaning it has many divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60). This makes it very convenient for calculations involving fractions, as many common fractions (like 1/2, 1/3, 1/4, 1/5, 1/6) can be expressed as exact sexagesimal fractions.