2D. If a letter be placed at the left of one of greater value, its value is to be taken from that of the greater. Thus, IV denotes four, IX nine, XL forty. 3D. If a letter be placed at the right of one of greater value, its value is to be united to that of the greater. Thus, VI denotes six, XI eleven, LX sixty. 4TH. If a letter be placed between two denoting greater values, its value is to be taken from the united value of the other two. Thus, XIV denotes fourteen, XIX nineteen. 5TH. A line over a letter increases its value a thousandfold. Thus, V denotes five thousand, X ten thousand. XXVII. Twenty-seven. DCCC. Eight hundred. XXVIII. Twenty-eight. DCCCC. XXIX. Twenty-nine. | M, or CIƆ, One thousand. Nine hundred. NOTE.-The Roman Notation is commonly used in numbering chapters, sections, books, and public documents. EXAMPLES. Express the following numbers by the Roman Notation. 1. Thirty-nine. 2. Fifty-seven. 6. One hundred twenty. 10. Nine hundred nineteen. 11. One thousand six hundred sixty-one. 12. Four thousand eight hundred eighty-eight. 14. The present year of the Christian era. ARABIC NOTATION. Art. 18. The symbols of the Arabic Notation are ten figures, viz. : 0 1 2 3 4 5 6 7 8 9 one, two, three, four, five, six, seven, eight, nine, naught. The first nine of these figures are called significant figures, because they signify some number. They are also called digits. The figure, 0, naught, is also called cipher and zero, because when alone it expresses no number. Art. 19. To express more than nine units, two or more figures must be combined, this is done on the following Principle. A figure at the left of units expresses tens; at the left of tens, hundreds; at the left of hundreds, thousands; at the left of thousands, ten thousands; &c. In general, a figure expresses a ten times greater quantity every time it is placed at the left of one more figure. Thus, ten is one ten no units, and is written with a 1 at the left of a 0; twenty is two tens no units, and is written with a 2 at the left of a 0, &c. Therefore 10 is ten; 20, twenty; 30, thirty; 40, forty; 50, fifty; 60, sixty; 70, seventy; 80, eighty; 90, ninety. All other numbers less than a hundred are expressed by placing a significant figure in the units' place. Thus, 11 is one ten one unit, or eleven; 24 is two tens four units, or twentyfour; &c. Hundreds are expressed by figures in the third place toward the left. Hence 1 at the left of two O's signifies one hundred no tens no units, or, simply, one hundred. Therefore, 100 is one hundred; 200, two hundred; 300, three hundred; 400, four hundred; 500, five hundred; &c. Thousands are expressed by figures in the fourth place toward the left. Thus, 1000 is one thousand; 2000, two thousand; &c. Tens of thousands are expressed by figures in the fifth place toward the left. Thus, 10000 is ten thousand; 20000, twenty thousand; &c. Hundreds of thousands are expressed by figures in the sixth place toward the left. Thus, 100000 is one hundred thousand; 200000, two hundred thousand; &c. Millions are expressed by figures in the seventh place toward the left. Thus, 1000000 is one million; 2000000, two million; &c. Hence, if we consider a ten, a hundred, a thousand, &c., as units of different values, it is plain that ten units of any order of value make one of the next higher order; that is, make a unit of ten times a greater value. Thus : Ten units Ten tens Ten hundreds Ten thousands &c. make one ten. make one hundred. make one thousand. make one ten-thousand. &c. Art. 20. The place of a figure is its position in a number, as determined by reckoning the number of figures it is removed from the units of that number. The value of a figure is its power to express quantity. Figures have two kinds of value, viz.: simple and local. The simple value of a figure is the quantity which it expresses when it is alone. The local value of a figure is the quantity which it expresses by occupying a place in a number. In the units' place of a number the simple and local value of a figure are the same. NUMERATION. Art. 21. Numeration is the art of reading numbers expressed by figures. To assist in reading and writing numbers in the Arabic Notation, the figures are arranged in groups, called periods, beginning at the place of units. There are two methods of grouping in use, viz.: the French and the English. FRENCH METHOD OF NUMERATION. Art. 22. In the French method of numeration three figures form a period. The right-hand figure of every period is the units of that period, the middle figure is its tens, and the left-hand figure is its hundreds. The names of the periods from right to left, are:— 7th period. 6th period. 5th period. 4th period. 3d period. 2d period. Quintillions.Quadrillions. Trillions. Billions. Millions. Thousands. 1st period. Units. This number is read thus:-Seven hundred eighty-four quintillions, two hundred ninety-six quadrillions, five hundred thirteen trillions, eight hundred fifty billions, three hundred seventyfive millions, four hundred thousand, six hundred ninety-eight. Art. 23. To read a simple whole number. Rule. Beginning at units, mark off the figures into periods of three, toward the left, naming the periods as you proceed. Then, beginning at the left, read and name each period in order, omitting the names of those filled with ciphers, and also the name of the units' period. NOTE.-It is best to omit the word and in reading the figures. |