Egyptian Numerals:
The ancient Egyptian (4000 BC) system was a pure additive system. Once the symbols are learned, all you have to do is add their values together. Although the actual symbols vary from source to source, here are some of the most common variations, and their corresponding values.

Symbol
Name	Astonished Person	Polliwog	Pointing Finger	Lotus Flower	Scroll	Heelbone	Staff
Value	1,000,000	100,000	10,000	1000	100	10	1

Thus, the Egyptian numeral for 4124 would be written as .

Find the value for each of the following Egyptian numerals:

a.		Answer --> 526
b.		Answer --> 201,102
c.		Answer --> 1,304,010

Babylonian Numerals:
The Babylonian (3000 BC) system took the idea of an additive system to a new level - a level that included the concept of place value. To create their numerals, the Babylonians took an stylus with a triangle-shaped end and stabbed it into a soft piece of clay. For simplicity, their numeration system consisted of exactly two symbols. The first symbol, which stood for 1, was made by a single vertical mark. Next, their symbol for a group of 10 was made by turning the stylus and stabbing the clay twice, so the narrow ends of the two marks touched.

Pictorially, here are the two Babylonian symbols and their values:

Symbol
Value	1	10

Our numeration system (the Hindu-Arabic system) organizes digits into place values corresponding to powers of 10. The number 5678 stands for 5000+600+70+8, which can be read 5×10³ + 6×10² + 7×10¹ + 8×10⁰. The Babylonian system assigns the digits into place values corresponding to powers of 60. Similar to our system, since 60⁰ = 1, the right-most column corresponds to the ones column. Then, going from right to left, the value of the columns are 60, 3600 (which is 60²), 216,000 (60³) and so on, as needed.

The greatest amount that can appear in any column is 59, which is indicated as below with 5 tens and 9 ones. The stacking of the digits is done to conserve space.

Next, the symbols are grouped into their place value columns, taking special care to leave enough space between the columns. Thus, the number      would stand for 2×60 + 21×1 = 120 + 21 = 141.

Find the value for each of the following Babylonian numerals.

a.		Answer --> 275
b.		Answer --> 36,803

This system has the advantage of being able to write large values with a relatively small amount of characters (in this case, two characters!). However, there are some inherent problems. What if we wanted to write 3601? We would have to have a single mark in the 3600 column and a single mark in the one's column. But, if we wrote      we would have the left hand mark in the 60's column, making the value 61, not 3601. Originally, the Babylonians used context to tell the difference between their representations for similar numbers. Later Babylonian (300 BC) systems contained a divider symbol that was made by turning the poking stylus diagonally and stabbing the clay twice. The divider would be used to indicate a skipped place value. Thus, later Babylonian systems would write 3601 as         . The Babylonian divider was an ingenious addition, but it was not used to indicate the absence of a digit at the end of a number. There was still no way, except for context, to distinguish between the values for 1 and 60.

Find the value for each of the following Babylonian numerals.

a.		Answer --> 14,401
b.		Answer --> 36,023

Last Updated: July 11, 2007