184 CHAPTER 4 Systems of Numeration is necessary. The remainder represents the number of units when the numeral is written in expanded form. Therefore, 2519 (41 60) (59 1). = × + × When written as a Babylonian numeral, 2519 is 7 Now try Exercise 27 Example 5 Using Division to Determine a Babylonian Numeral Write 5363 as a Babylonian numeral. Solution To begin, divide 5363 by the largest positional value less than or equal to 5363. That value is 3600. 5363 3600 1 with remainder 1763 ÷ = There is one group of 3600 in 5363. Next divide the remainder, 1763, by 60 to determine the number of groups of 60 in 1763. 1763 60 29 with remainder 23 ÷ = There are 29 groups of 60 with 23 units remaining. 5363 (1 3600) (29 60) (23 1) = × + × + × Thus, 5363 written as a Babylonian numeral is 7 Now try Exercise 29 Example 6 A Babylonian Numeral with a Blank Space Write 7223 as a Babylonian numeral. Solution As we did in the last example, we begin by dividing 7223 by 3600. 7223 3600 2 with remainder 23 ÷ = Therefore, there are two groups of 3600 in 7223. The next positional value in the Babylonian numeration system is 60. However, the remainder from the above division, 23, is less than 60. So there are zero groups of 60 in 7223 and 23 units remaining. Therefore, we can write 7223 as follows: 7223 (2 60 ) (0 60) (23 1) 2 = × + × + × Recall that the Babylonian numeration system does not contain a symbol for 0. Therefore, we will need to leave a larger blank space when writing the numeral. This larger blank space will indicate that there are no groups of 60s present in 7223. = × + + + × 7223 (2 60 ) (0 60) (23 1) 2 The larger blank space here represents 0 groups of 60. Thus, the answer is . 7 Now try Exercise 31 Learning Catalytics Keyword: Angel-SOM-4.2 (See Preface for additional details.) Mayan Numerals Another place-value system is the Mayan numeration system. The ancient ancestors of the Maya people, who lived in Mesoamerica for thousands of years, developed a sophisticated numeration system based on their religious and agricultural calendar. MATHEMATICS TODAY Numerals of the World Although most countries presently use a place-value numeration system with base 10, the numerals used for the digits differ by country. For example, although the people of Myanmar use the traditional Hindu–Arabic numerals, they also use the following numerals. 0 1 2 3 4 5 6 7 8 9 Why This Is Important Although the numerals used will vary from culture to culture, the underlying concept of number remains the same throughout the world. Peter Hermes Furian/123RF
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