186 CHAPTER 4 Systems of Numeration Example 9 From a Hindu–Arabic to a Mayan Numeral Write 4025 as a Mayan numeral. Solution To convert from a Hindu–Arabic to a Mayan numeral, we use a procedure similar to the one used to convert to a Babylonian numeral. The Mayan numeration system positional values are , 7200, 360, 20, 1. … The greatest positional value less than or equal to 4025 is 360. Divide 4025 by 360. 4025 360 11 with remainder 65 ÷ = There are 11 groups of 360 in 4025. Next, divide the remainder, 65, by 20. 65 20 3 with remainder 5 ÷ = There are 3 groups of 20 with five units remaining. 4025 (11 360) (3 20) (5 1) = × + × + × 4025 written as a Mayan numeral is 11 360 3 20 5 1 × × × ⎫ ⎬ ⎪ ⎭ ⎪ = 7 Now try Exercise 41 Timely Tip Notice that changing a numeral from the Babylonian or Mayan numeration system to the Hindu– Arabic (or decimal or base 10 ) system involves multiplication . Changing a numeral from the Hindu–Arabic system to the Babylonian or Mayan numeration system involves division . Example 10 From a Hindu–Arabic to Mayan Numeral Write 21,846 as a Mayan numeral. Solution To begin, divide 21,846 by the largest positional value less than or equal to 21,846. That value is 7200. 21,846 7200 3 with remainder 246 ÷ = There are 3 groups of 7200 in 21,846. The next positional value in the Mayan numeration system is 360. However, the remainder from the above division, 246, is less than 360. So there are zero groups of 360 in 21,846 with a remainder of 246. Next we divide 246 by 20. 246 20 12 with remainder 6. ÷ = There are 12 groups of 20 with 6 units remaining. 21,846 (3 7200) (0 360) (12 20) (6 1) = × + × + × + × 21,846 written as a Mayan numeral is 3 7200 0 360 12 20 6 1 × × × × ⎫ ⎬ ⎪⎪ ⎭ ⎪ ⎪ = 7 Now try Exercise 43 Instructor Resources for Section 4.2 in MyLab Math • Objective-Level Videos 4.2 • PowerPoint Lecture Slides 4.2 • MyLab Exercises and Assignments 4.2 Exercises Warm Up Exercises In Exercises 1–10, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. The most common place-value system is the decimal number system that uses a base of ________. 10 2. When we write 789 as (7 10 ) (8 10) (9 1) 2 × + × + × the number is written in ________ form. Expanded 3. In the numeral 234, the 2 represents 2 ________. Hundreds 4. In the numeral 234, the 3 represents 3 ________. Tens SECTION 4.2
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