# Babylonian Numeration System

## Timeline

The Babylonians began a numeration system somewhere around 1900-1800BC, which is one of the oldest number systems. This particular system is no longer used by the Babylonians because it was replaced by the Arabic numeration system. Babylonians stopped using this system around 539BC.

## Basis of the Numeration System

The Babylonians had a very advanced number system which was a base sixty system rather than a base ten, which is what we use today. The Babylonians developed a form of writing based on cuneiform. Cuneiform means "wedge shape" in Latin. They wrote these symbols on wet clay tablets which were baked in the hot sun.

## Functions

The Babylonians used this numeration system for other functions besides math. They used the base sixty in everyday life by dividing the day into twenty-four hours, each hour into sixty minutes and each minute into sixty seconds. The Babylonians would also keep track of money by writing their symbols on the clay tablets. Merchants would use them to keep track of their money and business transactions throughout the day.

## Calculations

Both multiplying and dividing the way the Babylonian's would is rather hard to understand. They had tables that would show multiples, squares, and reciprocals to aid them and help them while doing certian calculations.

## Multiplying

• The Babylonians used the formula: ab = [(a + b)2- a2- b2]/2 to make multiplication easier.
• Even better is their formula: ab = [(a + b)2- (a - b)2]/4 which shows that a table of squares is all that is necessary to multiply numbers, simply taking the difference of the two squares that were looked up in the table then taking a quarter of the answer.

## Dividing

Divison was a harder process than multiplication. The Babylonians did not have an algorithm for long division. Instead, they based their method on the fact that a/b=ax(1/b) so all that was necessary was the table of reciprocals.

• Decimals work better with a base sixty.
• Babylonian numeration system uses place value.

• The Babylonians lacked the number zero.

## Important Information

• The Babylonians did not have a symbol for zero, but they did use the idea of zero. When they wanted to express zero, they just left a blank space in the number they were writing.
• The Babylonian Empire was one of the great empires that dominated the region of Mesopotamia.
• Babylon was located in what is now the Iraqi region.

## Citations

- "Ancient Babylonia (Babylon the Great)." Ancient Babylonia (Babylon the Great). Web. 10 May 2016.

- "An Overview of Babylonian Mathematics." Babylonian Mathematics. Web. 10 May 2016.

- "Babylonia." Wikipedia. Wikimedia Foundation. Web. 09 May 2016.

- "Babylonian Culture." Art History Summary Periods and Movements through Time. 2012. Web. 10 May 2016.

-"Dividing Sign." Dividing Sign. Web. 10 May 2016.

- "Image Gallery:." British Museum. Web. 09 May 2016.

- "RelatedCliparts:." Multiplication Clip Art. Web. 10 May 2016.

- "The Saga of Mathematics: A Brief History." Babylonian Multiplication. Web. 09 May 2016.