of figures. When there are more than nine places of figures, it will be convenient to divide them into periods of three figures each, as in the following By this table we discover that each period, or group of three figures, takes a new name, by which means the numeration of all numbers is made to depend upon that of three figures. 6. The above method of numerating, by giving to each period of three figures an independent name, is due to the French. There is another method, sometimes used, called the English method. It consists in giving a new name to each period of six figures. The French way is the sim methods at one view in the following pler, and is generally adopted. We will exhibit the two How many do the English connect in a period? Which method is to be preferred? By the French method of numerating, how many figures are connected in a period? periods of three figures, the following numbers: let him be required to numerate and read, by dividing into 7. After the pupil has carefully examined this table, 3478567321752005 1347835674116 75456278327005717 467743486921785412123456489 45654213400100205437 633456267489136545 Let him also separate them into periods of six figures, according to the English method, and then numerate and read them. It will be seen, by reference to the foregoing tables, that the French and English methods of numeration agree as far as nine places of figures, which is as far as we generally wish to extend numbers in the ordinary business operations of life. Numbers could be chosen which should be widely different, and still would be read precisely the same by the two methods. For instance, the French method of reading 103900000000000 is the same as the English method of reading 103000900000000000000, each reading being one hundred and three trillions, nine hundred billions. The same is the case with infinite other numbers which might be selected. Hence the importance of knowing which system of numeration is employed. Twenty billions in the English system is a thousand times twenty billions in the French system. ROMAN NOTATION. 8. The Romans, as well as many other nations, expressed numbers by certain letters of the alphabet. The Romans made use of only seven capital letters, viz.: I for one; V for five; X for ten; L for fifty; C for one hundred ; D for five hundred; M for one thousand. The other numbers they expressed by various repetitions and combinations of these letters, as in the following 1 expressed by I. 2 " II. TABLE. As often as any character is repeated, so many By what means did the Romans express numbers? In this notation, how did repeating a letter affect the value which it represented? How was the value of a character affected when one of less value was placed before it? How when a character of less value was placed after it? How was the value affected by a bar drawn over it? ADDITION OF SIMPLE NUMBERS. 9. SIMPLE ADDITION is putting together several numbers of the same kind or denomination. The sum total which is obtained by adding several numbers together, is called the amount. Before explaining the method of adding numbers, we will show the use of the two symbols =, +. The symbol, is called the sign of equality, and when placed between two quantities, it indicates that they are equal. Thus $1=100 cents, implies that one dollar is equal to one hundred cents. The symbol +, is called the sign of addition, and when placed between two quantities, indicates that those quantities are to be added. Thus 3+4=7, denotes that the sum of 3 and 4 is equal to 7. The symbol meaning more. is generally read plus; a Latin word, What is simple addition? What is the result obtained by adding several numbers together, called? Describe the symbol of equality. Describe that of addition. By the assistance of these two symbols we may form the following |
