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 Understanding Place Value and Numeration Systems Deeper Understanding

### The Mayan Numeration System

The Mayan numeration system (c. 200 A.D.) was truly remarkable for its time. It is a positional system that includes a symbol for zero. Other numeration systems did not contain such ideas until around 800 A.D. The Mayan system is almost, although not entirely, a base-twenty system. It includes the following symbols for the numbers 0 through 19.

Larger numbers in this system are written using the "digits" above. Numbers are written vertically with the unit's position on the bottom. The values of the positions are shown in Table M-2. It is conjectured that the use of the positional values rather than the strict base-twenty values (202, 203, etc.) was due to the fact that 1 is approximately the number of days in a year. Examples M-1 and M-2 illustrate conversion between Mayan numerals and standard decimal numerals. For such conversions, one needs to consider the digit in each position and the value of that position.

Additions and subtractions can be carried out using Mayan numerals in a similar fashion to how these operations were performed using Egyptian and Roman numerals. Regroupings are performed as necessary. The Mayan system has the interesting property that not all numbers have unique representations. Examples can be found in the exercises.

Many calculators contain an integer division key that is useful in performing calculations such as those shown above. On many calculators, this key is marked with both the division symbol ( and the letters INT or Int. We illustrate the usefulness of the integer division key for Mayan numeral calculations in Example M-3.

### Mayan Numeral Problem Set

Complete these problems on a sheet of paper.

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