Babylonian Numbers โ The Sexagesimal Legacy
Convert between decimal and base-60 notation. Discover why we have 60 seconds in a minute and 360 degrees in a circle โ gifts from ancient Mesopotamia.
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60 has 12 divisors, making fractions easier than base-10. Plimpton 322 tablet (~1800 BCE) contains Pythagorean triples in sexagesimal. Our 60 sec/min and 360ยฐ circle come directly from Babylonian mathematics.
Ready to run the numbers?
Why: Babylonian numerals were used in ancient Mesopotamia for astronomy, commerce, and mathematics. Their base-60 system survives today in time and angles.
How: Divide by 60 repeatedly for decimalโBabylonian; multiply each digit by its place value (60^position) and sum for Babylonianโdecimal.
Run the calculator when you are ready.
Babylonian Numbers โ The Sexagesimal Legacy
Convert between decimal and base-60 notation. Discover why we have 60 seconds in a minute and 360 degrees in a circle โ gifts from ancient Mesopotamia.
Conversion Direction
Input Value
For educational and informational purposes only. Verify with a qualified professional.
๐งฎ Fascinating Math Facts
60 seconds in a minute and 60 minutes in an hour come from the Babylonian sexagesimal system
โ Timekeeping
The 360-degree circle equals 6 ร 60 โ a Babylonian invention still used today
โ Geometry
๐ Key Takeaways
- โข Babylonian numbers use base-60 (sexagesimal), unlike our base-10 decimal system.
- โข Only two symbols: vertical wedge (๐น) for 1 and chevron (๐) for 10.
- โข Each position represents a power of 60; place value increases left to right.
- โข Our 60 seconds/minute and 60 minutes/hour come from the Babylonian system.
- โข The 360-degree circle (6 ร 60) is another Babylonian legacy.
๐ก Did You Know?
๐ How It Works
To convert decimal to Babylonian: repeatedly divide by 60 and collect remainders in reverse order. To convert Babylonian to decimal: multiply each digit by its place value (60^position) and sum.
Example: 150 in decimal = 2ร60 + 30 = 2,30 in Babylonian. Use commas to separate sexagesimal digits.
๐ฏ Expert Tips
๐ก Use Commas or Semicolons
Babylonian notation uses 1,30 or 1;30 โ both are valid separators.
๐ก Digits 0โ59 Only
Each sexagesimal digit must be between 0 and 59.
๐ก No Negative Numbers
Ancient Babylonians did not use negative numbers.
๐ก Fractions
1,30 can mean 1 + 30/60 = 1.5 in decimal.
โ๏ธ Comparison Table
| Decimal | Babylonian |
|---|---|
| 60 | 1,0 |
| 100 | 1,40 |
| 3600 | 1,0,0 |
| 150 | 2,30 |
โ Frequently Asked Questions
Why did Babylonians use base-60?
60 has many divisors (1,2,3,4,5,6,10,12,15,20,30,60), making fraction calculations easier. It may have merged earlier base-10 and base-6 systems.
How did Babylonians write fractions?
Using the same sexagesimal system: 1,30 could mean 1 + 30/60 = 1.5 in decimal.
Did Babylonians have zero?
Early Babylonian math lacked zero. By ~700 BCE they used a spacer for empty positions, but not at the end of numbers.
How accurate were Babylonian calculations?
Very accurate. They calculated โ2 as 1;24,51,10 (โ1.41421296), correct to 6 decimal places.
What is cuneiform?
Wedge-shaped writing made by pressing a reed stylus into clay. The name comes from Latin cuneus meaning "wedge".
Where is sexagesimal used today?
Time (60 sec/min, 60 min/hr), angles (360ยฐ = 6ร60), and geographic coordinates.
๐ Key Stats
๐ Reference Sources
โ ๏ธ Disclaimer: This calculator provides educational conversions. For historical research, consult academic sources. Babylonian notation can have multiple interpretations for fractional values.
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