42. Twenty-two thousand, and two hundred.

43. Eleven thousand, and eleven.

44. Thirty-seven thousand, eight hundred and thirteen.

45. Seventy-three thousand, and thirty-one.

46. Ninety thousand, and seventy.

47. Nine hundred and sixty-two thousand.

48. Seven hundred and one thousand.

49. One hundred thousand, and seven hundred.

50. Eight hundred thousand, and seventy-three.

51. Three hundred and one thousand, and twenty-one. 52. Five hundred thousand, and four.

53. Six hundred and twenty thousand, and forty.

54. Four million, seven hundred and fifty-two thousand, four hundred and fifty-eight.

55. Seven million. Seven million, and seven.

56. Three million, thirty thousand, and twelve.

57. Nineteen million, six hundred thousand, five hundred and thirty.

58. Thirty million, ten thousand, one hundred and one. 59. Ninety million, nine thousand, and nine. 60. Seven hundred million, and seventy.

61. Six hundred and eighty-three million, four hundred and seventeen thousand, nine hundred and ninety-eight. 62. Eight hundred and seven million, five hundred and three thousand, and nine.

63. Five hundred million, twenty thousand, and three hundred.

64. Four hundred and twenty million, six thousand, and twenty-six.

65. Seven billion, eight hundred and forty-six million, seven hundred and ninety-two thousand, two hundred and thirty-four.

66. Three billion, thirty million, seven hundred and eight thousand, and five.

67. Twenty-one billion, six hundred and three million, four hundred thousand, and twenty.

68. Sixty-eight billion, five million, twenty thousand, and forty.

69. Three hundred and twenty-five billion, six hundred million, four thousand, and two hundred.

70. Seven hundred and one billion, and two.

71. Two hundred and nine billion, sixty thousand, and five hundred.

72. Three trillion, four hundred and ninety-three billion, eight hundred and sixty-seven million, four hundred and eighty-two thousand, nine hundred and eighty-nine.

73. Eighty trillion, sixty million, and two hundred. 74. Five hundred and nine trillion, ninety-nine billion, forty thousand, and forty-four.

75. Fourteen quadrillion, two hundred billion, five million, one hundred and six thousand, and ninety-six.

76. One hundred and nine quadrillion, three hundred and sixty trillion, eight billion, five hundred million, twenty-four thousand, seven hundred and one.

77. Write 107 million, 17 thousand, and 17.

78. Write 509 thousand, and ninety.

79. Write 1 trillion, 10 billion, 100 million, and 1 thousand.

80. Write 59 quadrillion, 7 trillion, 50 billion, 909 million, and 101 thousand.

81. Write 200 million, 666 thousand, and 905.

82. Write 99 trillion, and 40 thousand.

83. Write 769 billion, 101 million, 40 thousand, and 20. 84. Write 120 million, 1 thousand, and 10.

85. Write 5 trillion, 606 billion, 16 million, 5 thousand, and 9.

86. Write 14 quadrillion, 12 trillion, 3 billion, 13 million, and 1.

Elem. 2.

ROMAN NOTATION.

13. The Roman Notation employs seven letters to express numbers; these are I, V, X, L, C, D, M.

NOTE.-The Roman System of Notation is so called because it was used by the ancient Romans. It is now used to number chapters and divisions of books, etc.

I denotes one; V, five; X, ten; L, fifty; C, one hundred; D, five hundred; and M, one thousand.

Repeating a letter repeats its value; thus, II denotes two; XXX, thirty; CCCC, four hundred.

If a letter is placed before one of greater value, the less is taken from the greater; but if placed after, its value is added to the greater; thus, IV denotes four, while VI denotes six.

Read the following numbers:

1. XXXVII.

2. XLIX.

3. XCVIII.

4. CXVI.

5. CCXIX.

6. DCXXIV.

7. DCCCXI.

8. MDLXXIV.

9. MDCCXXII. 10. MDCCXLIV.

11. MDCCLXXVI.

12. MDCCCLXXIX.

Write the following in Roman Notation:

14. An Integer is a whole number. Numbers are either abstract or concrete.

15. An Abstract number is a number simply; as 5, 12, 20.

16. A Concrete number is a number applied to one or more objects; as 1 book, 5 yards, 12 men.

17. The name of the object of a concrete number is its denomination. Thus in 5 yards, the denomination is yards. Numbers are either simple or compound.

18. A Compound number is a concrete number made up of different denominations; as 4 bushels, 3 pecks, 1 quart. 19. There are four primary operations of Arithmetic; namely, Addition, Subtraction, Multiplication, and Division; these are called the Fundamental Rules.

QUESTIONS FOR REVIEW.

What is a unit? Of what does a number consist?

What is

Of what value and How do you read What is the largest

By two figures?

Arithmetic? Define Notation. What are figures? Name the figures in use. What are the first nine called? use is the cipher (0)? Define Numeration. numbers less than ten? Greater than ten? number that can be expressed by one figure? Three figures? What is a period? What does the right-hand figure of a period represent? The middle figure? The left-hand figure? What is the simple value of a figure? The local value? In what direction and in what ratio does the value of a figure increase? How many orders in a period? If an order, or any part of it, is wanting, how is its place filled? How are periods separated? Give the Rule for Notation. The Rule for Numeration.

What characters are employed in the Roman system of Notation? State what each of the seven letters denotes. What is the effect of repeating a letter? Of placing a letter before one of greater value? After one of greater value? (Let the teacher drill the class on the table of Roman Notation.)

What is an integer?

What is an abstract number? A concrete number? What is meant by the denomination of a number? Have abstract numbers a denomination? What is a compound number? What are the Fundamental Rules of arithmetic?