PART II CHAPTER I THE FUNDAMENTAL PROCESSES NOTATION AND NUMERATION 1. Write in as many ways as you can the number of the present year. Read 26,057; MDXCVII. Writing numbers is called notation. Reading numbers is called numeration. A regular plan of writing or reading numbers is called a system of notation or of numeration. There are two systems of notation and numeration in use in this country: the Arabic and the Roman. The Arabic system was invented by the ancient Hindus, the people of India. It was introduced into Europe by the Arabs, hence its name. The Roman system was used by the ancient Romans. The Arabic system is the one used in all common business transactions. The Roman system is used chiefly in the numbering of certain chapters and pages of books, and on the faces of clocks and watches. Read 349; CCCXLIX. Write eighty-eight in both Arabic and Roman notation. Which do you think the better system? Why? THE ARABIC SYSTEM 2. The characters, or figures, of the Arabic system are 1, 2, 3, 4, 5, 6, 7, 8, 9, called digits, and 0, called zero, or cipher. Ten ones, or units Ten tens Ten hundreds 1,000 thousands 1,000 millions = = 1 million; 1,000 × 1,000 1,000,000. = 1 billion; 1,000 × 1,000,000 = 1,000,000,000. The use of numbers higher than millions is rare, though the following numbers are found by using 1,000 as a multiplier: billions, trillions, quadrillions, quintillions, sextillions, septillions, octillions, nonillions, and decillions. 1 decillion would contain 33 ciphers. The Arabic system is called a decimal system (from the Latin word decem, meaning "ten ") because it is a system of tens, each place having a value ten times greater or ten times less than the one next to it. The word digit means "finger." It indicates that the decimal system grew out of the custom of counting on the fingers. Numbers as written by the Arabic system are divided into periods of three figures each. According to its position each figure stands for units, tens, or hundreds of its period. In 3,126,374,201 the value of each figure is as follows: 3. Each period is read as a separate number followed by the name of the period, excepting that the name of the unit's period is not read, but is "understood." The number above is read: "Three billion, one hundred twenty-six million, three hundred seventy-four thousand, two hundred one." The cipher is used merely to fill vacant spaces and is not read. The places of the figures in a number are called orders. In reading numbers from left to right, a figure in unit's place of any period is called a figure of the first order. A figure in ten's place is called a figure of the second order. A figure in hundred's place is called a figure of the third order, and so on. 2. Express with figures: 7 billion, 80 million, 2 hundred thousand, 50. 20 billion, 3 million, 15 thousand, 8. 215 billion, 0 million, 140 thousand, 4 hundred. 305 million, 1 thousand, 11. 5 million, 5 thousand, 5 hundred, 5. 3. Write in words: 206,937. 92,010,005. 209,387,016. 587,009,307. 60,215,840,075. 40,003,090. 1,002,003,040. 26,807,243,201. THE ROMAN SYSTEM 5. The Roman notation uses seven letters, namely: These letters are combined to represent other numbers according to the following principles : (1) When a letter is followed by the same letter or by a letter of less value, it indicates that the values of the letters are added. Thus, II represents 2; VI, 6; XXX, 30; XV, 15; LX, 60; CX, 110; DC, 600. (2) When a letter is followed by a letter of greater value, its value is to be taken from that of the greater. Thus, IV represents 4; IX, 9; XL, 40; XC, 90; CD, 400; CM, 900. (3) Placing a dash over a letter multiplies its value by 1,000. Thus, V represents 5,000; X, 10,000; IV, 4,000. |