Babylonian Numerals

The Babylonian number system used a base sixty system. The Babylonians used two symbols to represent all their numbers, a one symbol and a ten symbol. For numbers between one and sixty, the Babylonians used these symbols to form numbers by repetition and addition. For numbers greater than sixty, they used the same symbols in other place values. A number of this type is expressed as two groups of symbols, one group representing the number of 60s the other the number of 1s, these are added to find the value of the number.

The Babylonian ones symbol is
The Babylonian tens symbol is
Below are some of the Babylonian place values, to assemble a Babylonian number you first find the largest base 60 place value you can subtract from the number, you then move on to the next place value at each place value you note the number of times it goes into what remains from the previous subtraction. You then can express the number as groups of Babylonian symbols, the first group showing how many times the highest place value subtracted out of the number, the next group showning the next highest place value and so on for all the place values you observed.
60^4 60^3 60^2 60^1 60^0 1/60^1 1/60^2 1/60^3
12,960,000 216,000 3600 60 1 1/60 1/3600 1/216,000
Below is an example of the steps to turn a Hindu Arabic number into Babylonian notation. For this example, the number 236,378 will be converted into Babylonian numbers.
place value 60^3 60^2 60^1 60^0
starting number 236,378 20,378 2,378 38
place value being subtracted 216,000 3,600 60 1
difference 20,378 2,378 38 0
number of times place value goes into starting number 1 5 39 38
number in Babylonian numerals
Because Babylonian numerals can be cumbersome, it is common to represent Babylonian numbers in Neugebauer Notation. This is done by taking the "number of times place value goes into starting number" value for each place value and seperating them by commas and putting a semicolon to show were the fractional part of the number starts. For the number from the last example, the Neugebauer form is 1,5,39,38.
To convert a number in Neugebauer Notation or Babylonian numerals into Hindu Arabic, you reverse the conversion process. You add the appropriate number of each place value together to get the Hindu Arabic value. In the example of 2,1,12,14 you add, 2*216,000+1*3,600+12*60+14*1 to get the Hindu Arabic value of 436,334.

Exercises

For each value given, convert it to Babylonian notation and Neugebauer Notation,
12,333,564=
36=
15/30=
For each value given, convert to Hindu Arabic and Babylonian Notation,
1,2,3,4;30=
2,3;35=
2,3=
For each value given, convert to Hindu Arabic and Neugebauer Notation,
=
=
       =
On to Babylonian Equations