Category Archives: Numeration Systems

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A numeration system is a logically organized collection of numerals. In my everyday life I use numbers to represent numerals, but numerals can also be written as symbols.  Egyptian numeration, Roman numeration, Babylonian numeration, and Mayan numeration systems all use written symbols for numerals. These systems have a unique organized collection of written symbols.

The Eqyptian and Roman numeration systems use symbols in a base-ten system. This means that each symbol stands for a power of ten (10, 10×10, 10x10x10, …). Although the Roman’s used a base-ten system, they modified it so that there are symbols for 5, 50, and 500. The Egyptian numeration system has seven symbols: the astonished man, tadpole, pointing finger, lotus flower, coiled rope, heel bone, and the stick. Each of these symbols represents a different number. For example the astonished man = 1,000,000, the tadpole = 100,000, the pointing finger = 10,000, the lotus flower = 1,000, the coiled rope = 100, the heel bone = 10, and the stick = 1. The Roman numeration system also has seven common symbols: I, V, X, L, C, D, and M; each symbol equals a different number. For example the I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1,000. Visualizing the symbols and the number they represent helps to understand the organized collection of numerals in the Egyptian and Roman numeration systems.

    The Babylonian numeration system is unlike the Egyptian and Roman systems because it uses symbols to represent base-sixty. A base-sixty system means that each symbol represents a power of sixty (60, 60×60, 60x60x60, …). There are basic symbols for 1-59; a martini glass looking symbol stands for 1 and a boomerang looking symbol stands for 10. The basic symbols for 1-59 and place value help to write numbers greater than 59. The standard way to read Babylonian symbols is from left to right. For example if there was two martini glass looking symbols on the left and one boomerang looking symbol plus five smaller martini glass looking symbols this would equal 135. In this case the two martini glass looking symbols on the left stand for 120 because each symbol alone stands for 60. This is where the concept of place value is important because now there are two meanings for the same symbol. The two larger martini glasses stand for 60, the boomerang symbol stands for 10, and the smaller martini glass symbols stand for 1.  The picture provided helps to explain the previous sentences.

The Mayan system is also very different because it uses a modified base-twenty system (20, 20×20, 20x20x20, …).  There are 20 basic symbols for the numbers 0-19; there is an oval that stands for 0, a dot that stands for 1, and a horizontal line that stands for 5. You stack the symbols vertically to add them together. For example 19 would be represented by three horizontal lines (5×3=15) plus four dots (1×4=4). To write numbers greater than 19, they used their basic symbols and place value. They wrote the symbols vertically with one symbol above another and had the powers of the base increasing from bottom to top. This means that the symbols in the bottom position stands for the number of units, the symbols on the second position stands for the number of 20’s and the third position stands for 18×20 instead of 20×20 because the Mayan calender had 18 months of 20 days each. This can be confusing because of the complex rules, but a picture of an example will help to explain.

 These numeration systems take time, effort, and patience to fully understand!

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