NOTATION AND NUMERATION OF UNITED

STATES MONEY.

21. The currency of the United States has a decimal system of notation, dollars being written as whole numbers and cents as decimal parts of a dollar.

22. The dollar sign is $. It is written before the number.

Thus, $25 is read twenty-five dollars.

23. In notation of United States currency a period, called the decimal point, is placed before the cents.

The dollars are written at the left of the decimal point. The first two places at the right of the decimal point express cents, and the third, tenths of a cent or mills.

Thus, $10.485 is read ten dollars, forty-eight cents, five mills.

24. When the number of cents is less than ten, a cipher must be written in the first place at the right of the decimal point.

Thus, Five dollars five cents is written $5.05.

26. Write the following:

1. Fifteen dollars, twelve cents. Eighteen dollars, eight cents. Twenty-four dollars, eight cents.

2. Thirty-four dollars, thirty cents. Fifty-five dollars, twenty cents. Nineteen dollars, thirty-eight cents.

3. Forty dollars, four cents. Ninety-nine dollars, nine cents. Sixty-four dollars, eleven cents.

4. Four hundred dollars, eight cents. Seven hundred dollars. Seventeen dollars, eight cents, eight mills.

5. Two hundred thirty-eight dollars, twenty cents, five mills. Ninety-three dollars, forty cents, eight mills.

6. Three hundred ninety-one dollars, forty-eight cents, three mills. Sixty-seven dollars,sixty-seven cents, three mills.

7. Four thousand three hundred twenty dollars, eight cents. Fifty-nine dollars, twenty cents, seven mills.

8. One thousand two hundred forty-nine dollars, nine cents, five mills. Forty-seven dollars, ninety cents, five mills.

9. Eighty-four thousand three hundred dollars, nine cents. Thirty dollars, nine cents, nine mills.

10. Fifty-five thousand eight hundred sixteen dollars, five cents. One thousand dollars, ten cents, five mills.

THE ROMAN SYSTEM.

27. This system uses seven capital letters to express numbers, viz.:

C, D,

Letters, I, V1 X, L, M. Values, 1, 5, 10, 50, 100, 500, 1000.

23. The following principles are followed in combining the letters:

PRINCIPLES.

1. Repeating a letter repeats its value.

Thus, I represents one; II, two; III, three; X, ten; XX, twenty. 2. When a letter is placed before another of greater value, its value is to be taken from that of the greater.

Thus, IV represents four; IX, nine; XIX, nineteen; XL, forty. 3. When a letter is placed after another of greater value, their values are to be united.

Thus, VII represents seven; XV, fifteen; LXXX, eighty.

4. A bar placed over a letter increases its value a thousandfold.

Thus, V represents five thousand; L, fifty thousand; M, one million.

29. Read the following numbers:

XVII; XXV; LXXX; XIX; XXIX; XLV; CXV; XCV; LXXIX; CXIX; XCIX; XLIV; CCCIV; CCXLIV; CCCCXC; DCCLXXXIX; XDCCCLXXII.

Express the following numbers by the Roman notation: 13, 24, 71, 68, 132, 514, 244, 555, 617, 1040, 7216, 2899.

ADDITION.

30. 1. How many apples are 3 apples and 2 apples?

2. How many books are 3 books and 4 books?

3. How many leaves are 2 leaves and 3 leaves?

4. How many oranges are 4 oranges and 2 oranges?

5. What have you been doing with the numbers given above?

6. Why can you not tell how many 5 cents and 4 rabbits are?

7. What kind of numbers only can be united?

31. The process of finding a number which is equal to two or more given numbers is called Addition.

32. The result obtained by adding is called the Sum, or Amount.

33. The numbers added are called Addends.

34. The Sign of Addition is an upright cross +. It is called plus, and is placed between the numbers to be added. Thus, 3 + 7 is read 3 plus 7, and it means that 3 and 7 are to be added."

35. The Sign of Equality is two equal short horizontal lines: =. It is read equals or is equal to.

Thus, 3+ 7 = 10 is read 3 plus 7 equals 10.

36. Any expression of equality is called an Equation.

Thus, 3+7=10 and 5 + 4 = 9 are equations.

37. Numbers that have the same unit are called Like Numbers.

Thus, $7 and $5 are like numbers; so also are 15 pounds and 8 pounds.

38. PRINCIPLES.

1. Only like numbers can be added.

2. The sum and the addends must be like numbers.

DRILL EXERCISES.

39. The student should practice adding the following numbers daily until he can tell the sums at a glance.