The Mayans devised a counting system that was able to represent very large numbers by using only 3 symbols, a dot, a bar, and a symbol for zero, or completion, usually a shell. The chart above shows the first complete cycle of numbers. Like our numbering system, they used place values to expand this system to allow the expression of very large values. Their system has two significant differences from the system we use: 1) the place values are arranged vertically, and 2) they use a base 20, or vigesimal, system. This means that, instead of the number in the second postion having a value 10 times that of the numeral (as in 11 - 1 × 10 + 1 × 1), in the Mayan system, the number in the second place has a value 20 times the value of the numeral. The number in the third place has a value of (20)2, or 400, times the value of the numeral. This principle is illustrated in the chart below.