Through the Victory Book Campaign BUSINESS ARITHMETIC CHAPTER I NUMBERS AND NUMERALS 1. The Decimal Number System. To secure a thorough knowledge of the Arithmetic of Business it is well to learn something of the nature and history of our number system. This system is called the decimal number system because the number ten is used as its base. That is, we first count to ten, then count ten more, and call the result twenty, or two tens. We then say twenty-one, or twenty and one, twenty-two, or twenty and two, and so on until we get twenty and ten, which is called thirty. In this manner the process is continued by counting repeatedly to ten and adding each ten to the preceding result until ten times ten, or one hundred, is reached, and so on indefinitely. 2. The Arabic Notation. The Arabic notation is best understood by studying an example. In the number 777,777 the numeral 7 to the right represents seven ones or units. The next numeral represents seven tens, the next seven hundreds, and so on. That is, any one of the numerals 7 used in writing this number represents ten times as much as the next one to the right of it. 3. The Principle of Place Value. — The example of the preceding paragraph illustrates the so-called principle of place value, according to which a numeral in the first place to the right represents ones, in the second place, tens, in the third place, hundreds, in the fourth place, thousands, and so on. By using the principle of place value, any integral number whatever can be expressed by means of the ten characters: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. 4. The Order of a Figure. In a whole number the figure in the first place to the right is said to be of the first order, the figure in the second place to be of the second order, and so on. Thus, in the number 123 456, 6 is of the first order, 5 of the second, 4 of the third, 3 of the fourth, and so on. 5. Periods. For the sake of convenience in reading large numbers, groups of three, called periods, are pointed off by means of commas or by extra spaces. The first period to the right represents ones, the second period, thousands, etc. 6. Reading Numbers. - Numbers are read as simply as is compatible with clearness. In reading whole numbers the word and is never used between figures of different order. Thus we say three hundred fifty-one, not three hundred and fifty-one. In reading a telephone number, such as 3758, we may say three, seven, five, eight. In reading a number like 374, we often say three, seventy-four. A number like 24,680 may be read twenty-four, six eighty. The number 196,483 may be read one ninety-six, four eighty-three. In dictating long tabulations such methods of reading numbers are usually used. Dictate the following numbers while some one else writes them down. Then check by having them dictated back. 7. Roman Numerals. - The numerals used by the Romans are still used in a few rare instances. The chapters of a book, the years of laying cornerstones of buildings, the value of paper money, the hours on the faces of most clocks are represented by Roman numerals. The characters used in the Roman notation are the following: . A stroke above any one of these, except I, multiplies its value by The principles according to which these characters are combined to represent other numbers are illustrated in the following: 1. If a character is repeated, the number represented by the character is multiplied by the number of times it is used. That is, XX = 2 x 10 = 20 and CCC = 3 x 100 = 300. 2. If a character representing a smaller number stands to the left of one representing a larger number, it is subtracted. 3. If a character representing a smaller number stands to the right of one representing a larger number, and does not at the same time stand to the left of one representing a larger number, it is added. = 5+1, and CXII = Thus, VI VIII = 8 IX XIV = 14 LXIV = 243 = 9 On timepieces IIII is sometimes used instead of IV. DCCLXII = 762 The principle of place value (§ 3) which is characteristic of the Arabic notation is entirely absent from the Roman notation. Thus, V represents five units no matter in what position it stands, though its position indicates whether it is to be added or subtracted. EXERCISES Read the following Roman numerals: 1. CXIV 5. DC 9. CXC 13. VMDCCC 2. CCXIX 6. DCCCLXVI 10. MCMXLV 14. XXVMXV 3. CCXL 7. MD 11. MMXIX 15. XLMMD Write the following in Arabic numerals : 37. Four hundred sixty-four thousand one hundred fifty-two. 38. Thirty-five thousand sixty-nine. 39. Seventeen hundred eighty-five. 40. Ninety-four hundred sixty-two. 41. Five million thirty-two thousand three hundred eighty. 42. Fifty-four million six thousand eight. 43. Two hundred thirty million sixteen thousand seventy. 44. Eight hundred thirty-six thousand two hundred ninety-one. 45. Three hundred two thousand six hundred fifteen. 46. Seventy-seven hundred ninety-eight. 47. Six hundred twenty-nine thousand two hundred forty-five. 48. Seven million two hundred thousand one hundred ninety-six. 49. Seventy-six million six thousand seventy-one. 50. One hundred thousand eighty-six. 51. Two hundred seventeen million seventy-five thousand eight hundred four. 52. Twelve million six thousand forty-seven. 53. One million eight hundred forty thousand. |