How to Convert the Base-10 Number 5160 to a Mayan Numeral

Question

Write the number 5160 as a Mayan numeral.

Accepted Answer

A Mayan numeral consisting of: 1 dot in the 18×20² (7200) place, 4 bars and 1 dot (21) in the 20² (400) place, 1 bar and 1 dot (6) in the 20¹ (20) place, and 0 shells in the 20⁰ (1) place. Visually: 100 100 (dot) above 100 200 (4 bars + 1 dot) above 100 300 (1 bar + 1 dot) above 100 400 (shell symbol)

Answer

Step 1: Recall the Mayan numeral system is a vigesimal (base-20) system with a modified place value for the third digit (×18 instead of ×20 to align with their calendar), so the place values are 1, 20, 18×20=360, 18×20²=7200, etc. Step 2: Divide 5160 by the largest place value less than it, which is 360: 5160 ÷ 360 = 14, remainder 120. Step 3: Now divide the remainder 120 by the next place value, 20: 120 ÷ 20 = 6, remainder 0. Step 4: The final remainder 0 is the value for the 1s place. Step 5: Convert each quotient to Mayan symbols: 14 is 2 full bars (each bar = 5) and 4 dots (2×5 + 4 =14), 6 is 1 bar and 1 dot (5+1=6), and 0 is represented by a shell symbol. Since 5160 is less than 7200, the highest place value used is 360, so we start with the 360 place symbol, then 20 place, then 1s place.