4.2 Place-Value or Positional-Value Numeration Systems 185 The numerals in this system are written vertically rather than horizontally, with the units position on the bottom. In the Mayan system, the numeral in the bottom row is to be multiplied by 1. The numeral in the second row from the bottom is to be multiplied by 20. The numeral in the third row is to be multiplied by 18 20, × or 360. You probably expected the numeral in the third row to be multiplied by 202 rather than 18 20. × It is believed that the Mayans used 18 20 × so that their numeration system would conform to their calendar of 360 days. The positional values greater than 18 20 × are 18 20 ,18 20 , 2 3 × × and so on. Positional Values in the Mayan System 18 (20) ,3 … × 18 (20) ,2 × 18 20, × 20, 1 or … 144,000, 7200, 360, 20, 1 The digits 0, 1, 2, 3, ,… 19 of the Mayan system are formed by a simple grouping of dots and lines, as shown in Table 4.6. Table 4.6 Mayan Numerals 0123456789 10 11 12 13 14 15 16 17 18 19 Example 7 The Mayan System: A Positional-Value System Write as a Hindu–Arabic numeral. Solution In the Mayan numeration system, the first three positional values are 18 20 20 1 × = × × = = × = = × = 11 (18 20) 3960 3 20 60 16 1 16 4036 7 Now try Exercise 33 Example 8 From a Mayan to a Hindu–Arabic Numeral Write as a Hindu–Arabic numeral. Solution = × × = = × × = = × = = × = 2 [18 (20) ] 14,400 8 (18 20) 2880 0 20 0 4 1 4 17,284 2 7 Now try Exercise 35 Did You Know? Mayan Numerals In addition to their base 20 numerals, the Maya people had a holy numeration system used by priests to create and maintain calendars. They used a special set of hieroglyphs that consisted of pictograms of Mayan gods. For example, in the diagram above, the number 3 represents the god of wind and rain, the number 4 represents the god of sun. Milagli/Shutterstock
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