What Is The Mayan Decimal System

The ancient Maya used a mathematical system that is “vigesimal.” A vigesimal counting system is based on 20 units (0 - 19), instead of the 10 unit (0 - 9) based counting system that we use today called the decimal system.
The decimal mathematical system widely used today is believed to have possibly originated by counting the number of fingers that the average person has. Counting with our fingers gives us our ten unit based metric system. It is believed that the Maya possibly began counting with both their fingers and toes, giving them their twenty based 'vigesimal' system. Their counting system is based on groups of twenty, instead of our modern ten.
When we count using our decimal system, we count to ten and then we add one value to
1 x10=100 x10=1,000 x10=10,000 and so on.
Decimal tiers. 1 value from tier 2 is 10 and 1 value from tier 1 is 1, One value each from tier 1 and 2 equals 11 (10 + 1 = 11 ).

Although we users of the modern decimal system are not used to thinking of our counting in tiers or levels, it does help us understand how the count using the Maya vigesimal system. Just as the decimal system goes by tiers of ten: 1, 10, 100, 1000, 10000, etc., the Maya vigesimal system goes by tiers of twenty: 1, 20, 400, 8000, 160000, etc..

Comparison of decimal and vigesimal
For the number “21,” both systems used the twenty from tier 2 and the one from tier 1 to make: 20 + 1 = 21. Except with the Maya vigesimal system, they used 1 value on tier 1 and 1 value on tier 2. The decimal system uses 1 value on tier 1 and 2 values on tier2.
To make “11,” the decimal system uses 1 value from tier 2 equaling 10 and 1 value from tier 1. (10 + 1 = 11). The difference in the Maya vigesimal system that value of 11 is actually calculated with two 'fives' from tier 1 and an 'one' also from tier 1. On their system, if the count hasn't reached or passed the value of 20, it remains on the first tier. Additionally, the value of 20 was divided by 4 values of 5.
To represent these values, the Maya came up with two symbols of which they use, a dot and a bar. The Maya used a system of bars and dots for their numbers, instead of representing them by different symbols as it is done in our numbering system. A system the we adapted from the Romans. Each 'dot' in the Maya system represents the value of 1 unit on a given tier. Each bar represents the value of 5 dots of the tier below it.
1 dot equals 1 and 1 bar equals 5