176 CHAPTER 4 Systems of Numeration Chinese numerals are always written vertically. The numeral on top usually will be from 1 to 9 inclusive. This numeral is to be multiplied by the power of 10 below it. Thus, 20 is written 2 10 20 } × = and 400 is written 4 100 400 } × = Table 4.3 Traditional Chinese Numerals Traditional Chinese numerals Hindu–Arabic numerals 0 1 2 3 4 5 6 7 8 9 10 100 1000 MATHEMATICS TODAY Hindu–Arabic Numerals Around the World Although languages vary from country to country, most countries currently use Hindu–Arabic numerals. Some countries use both Hindu–Arabic numerals and their own country’s numerals on signs and on automobile license plates. Above is a photo of a license plate in China and a photo of a license plate in Thailand. Why This Is Important Although languages vary all over the world, most countries use the same numeration system—the Hindu– Arabic numeration system. m License plate in China. m License plate in Thailand. Example 7 A Traditional Chinese Numeral Write 538 as a Chinese numeral. Solution 538 500 5 100 30 3 10 8 8 { { = = = = ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ 7 Now try Exercise 53 When writing traditional Chinese numerals, the units digit is never multiplied by a power of the base. Note that in Example 7 the units digit, the 8, was not multiplied by a power of the base. When writing Chinese numerals, there are some special cases that need to be considered. When writing a numeral between 11 and 19 it is not necessary to include the 1 before the 10. Thus, 18 would be written rather than . Another special case involves the use of zero. When more than one consecutive zero occurs (except at the end of a numeral) you need to write a zero, but only once for two or more consecutive zeros. Zeros are not included at the end of numerals. The top two illustrations that follow show how zeros are used within a numeral, and the bottom two show that zeros are not used at the end of a numeral. 406 = 4 100 400 } × = × = } 0 10 0 = } 6 6 4006 = 4 1000 4000 } × = } 0 100 0 × = } 6 6 = 0 10 0 × = 460 = 4 100 400 } × = 6 10 60 } × = 4600 = 4 1000 4000 } × = 6 100 600 } × =
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