14 DEFINITIONS - NOTATION AND NUMERATION 13. Give the names of the periods, in succession, beginning at the left. Give the 14. What is the name of the first period? number and name of each order in this period, thus: The name of the first period is units. The name of the second order is tens. The name of the third order is hundreds. 15. What is the name of the second period? Give the number and name of each order in this period. 16. What is the name of the third period? Give the number and name of each order in this period. 17. What is the name of the fourth period? Give the number and name of each order in this period. Notice that the name of the first order in each period is the same as the name of the period; that the name of the second order in each period after the first is ten, with the name of the period added; that the name of the third order in each period after the first is hundred, with the name of the period added. RULE FOR NUMERATION: Beginning at the units' order, point off the number into periods of three orders each. Beginning at the left, read each period as if it stood alone and add the name of the period. Read the following numbers from the book : 18. 203,417,256 The third period, standing alone, is read, two hundred three; on adding the name of the period, it is read, two hundred three million. The second period, standing alone, is read, four hundred seventeen; on adding the name of the period, it is read four hundred seventeen thousand. The first period, standing alone, is read, two hundred fifty-six. In reading a number the name of the units' period is omitted. 19. 20. 56,400,321,256 127,370,209,127 21. 21,257,048,563,047 22. 478,000,397,256,007 23. 421,057,400,320,000 20,003,900,708,516 24. 25. 106,100,400,300,260 26. 207,000,123,405,000 Before attempting to read the entire numbers, read the numbers in each period without adding the name of the period. Begin at the top and read downwards; as, two hundred fifty-six, one hundred twenty-seven, forty-seven, seven, naught, five hundred sixteen, two hundred sixty, naught. Whenever, in reading a number, you reach a period of ciphers, omit it and read the next period. TO THE TEACHER. Put other numbers on the board and require pupils to read them at sight, until they can read any number to one billion readily and accurately. ARABIC NOTATION 3. To write units of any period requires one figure in that period; to write tens or tens and units of any period requires two figures in that period; to write hundreds, hundreds and tens, hundreds and units, or hundreds, tens, and units, of any period requires three figures in that period. If there are vacant places, they should be filled with ciphers. Write the names of the first three periods in order; under these names write the following numbers in their proper places: 16 DEFINITIONS-NOTATION AND NUMERATION 12. Twenty-five thousand, four hundred six. 14. Two million, twenty-two thousand, four hundred six. 15. Twenty-two million, two thousand, four hundred six. 16. Two hundred twenty million, twenty thousand, four hundred six. 17. Fifteen thousand, nine hundred forty-eight. 18. Two hundred thousand. 19. Four million, four thousand, four hundred. 20. Four hundred thousand six. 21. Nine hundred eight million, fourteen thousand, five hundred. 22. Thirteen thousand eighteen. 23. Eighteen thousand two. 24. Five hundred seventeen million, three hundred sixtyeight thousand, seven hundred ninety-nine. 25. Three hundred million, eight hundred seventeen thousand, eight hundred seven. 26. Nine hundred ninety-nine million, nine hundred ninetynine thousand, ninety-nine. TO THE TEACHER. Read the following numbers to pupils, requiring the numbers to be written as read. When written, require pupils to read them. 27. 28. 40,062 29. 146,350 30. 107,009 785,020 634,009 780,350 609,095 2,469,304 15,000,270 27,039,009 65,078,027 5,860,000 7,200,000 2,794,352 4,000,000 RULE FOR NOTATION: Begin at the left hand and write the hundreds, tens, and units of each period in succession, filling vacant orders with ciphers. ROMAN SYSTEM OF NOTATION 4. The seven letters used in the Roman system are: Letters: I, V, X, L, C, D, M. Values: 1, 5, 10, 50, 100, 500, 1000. The following principles govern the use of these letters in expressing numbers: = 1. Repeating a letter repeats its value. XX = 20. II 2. 2. When a letter is placed after one of greater value, the two express the sum of their values. XV 15. CL = = 150. 3. When a letter is placed before one of greater value, the two express the difference of their values. IX = 9. IV = 4. 4. When a letter is placed between two letters of greater value, its value is to be taken from the sum of the other two. : 19. XIX = 5. Placing a dash over a letter multiplies its value by one thousand. X = 10,000. M = 1,000,000. The following table further illustrates the system : 6. Express the following numbers by the Arabic notaXIX, XXVIII, XXIX, XXXIX, CIX, XCI, CC, DCL, M, MC, T, MM, UMII, MDCCCCV. tion 7. Express by Roman characters all numbers from 1 to 50; from 51 to 100. 8. Express in the Roman notation : 106, 254, 372, 409, 698, 785, 843, 967, 1909, 10,000. HARVEY'S AR. II- 2 ADDITION 5. Addition is the process of uniting two or more numbers into one number. The numbers added are called addends. 2 1 Addends The sum is the number obtained by addition.. 5 8 Sum Only like numbers, that is, numbers having the same unit, can be added. THE FORTY-FIVE COMBINATIONS 6. In rapid addition of numbers, a knowledge of the sum of any two single-figure numbers is a necessity. There are forty-five combinations. Thirty-six of these combinations are given in the addition table below, and should be memorized. The other nine, combinations of 1 and each of the digits, are not given. 13. 26 3+7 4+8 5+9 14. 2+7 3+8 4+9 TO THE TEACHER. For rapid drill, place the table on the board; point to different combinations, requiring individual pupils to give sum of each combination as it is pointed out. Give the combinations orally and have pupils give sums. Use the following drill table in the same manner. 15. 2+8 3+ 9 16. 2+9 |