31. Four hundred million, three hundred twenty-nine. 32. Fifty-five billion, two hundred million, nine hundred eighty-four thousand, seventy-five.

33. Six hundred ninety-five million, eight hundred thousand, four hundred forty-one.

34. Seventy million, seventy thousand, seven.

35. Eighty-five billion, eight million, seven thousand two hundred ninety-four.

36. Fifty-two billion, two hundred six million, forty thousand, eight hundred five.

NOTATION AND NUMERATION OF UNITED
STATES MONEY.

33. In the currency of the United States

10 mills make 1 cent.

10 cents make 1 dime.

10 dimes make 1 dollar.

100 cents make 1 dollar.

34. The Sign of Dollars is $. It is written before the number.

Thus, $24 is read, twenty-four dollars.

35. In writing cents and mills a period called the decimal point is placed before the number.

Cents occupy the first two places at the right of the decimal point, and mills the third.

Thus, $.24 is read, twenty-four cents; $3.185 is read, three dollars, eighteen cents, five mills.

36. If 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, four dollars, three cents, five mills, is written, $4.035.

Write the following:

1. Eighteen dollars, twenty-four cents. 2. Twenty-six dollars, thirty-six cents.

3. Fifty-one dollars, five cents, five mills.

4. Thirty-eight dollars, six cents, three mills. 5. Twenty-seven cents, eight mills.

6. Thirty-four cents, nine mills.

7. Eighty-six dollars, five cents, two mills.

8. Twenty-one dollars, twenty-one cents, one mill.

9. Thirty-seven dollars, eighteen cents, eight mills. 10. Forty-nine dollars, nine cents, six mills.

ROMAN SYSTEM.

38. Roman Notation is the method of expressing numbers by means of letters.

It is called the Roman Notation because it was originally used by the ancient Romans.

39. In this system seven capital letters are used to express numbers, viz:

LETTERS:

I, V, X, L, C, D, M. VALUES: 1, 5, 10, 50, 100, 500, 1000.

40. By combining these letters according to certain principles, any number can be expressed.

PRINCIPLES.-1. When a letter is repeated its value is re

peated.

Thus, X represents ten; XX, twenty; XXX, thirty; C, one hundred; CC, two hundred.

2. When a letter is placed before another of greater value its value is to be taken from that of the greater.

Thus, I represents one and V five, but IV represents four; IX, nine; XIX, nineteen; XL, forty; XC, ninety.

3. When a letter is placed after another of greater value their values are to be united.

Thus, XV represents fifteen; LXX, seventy; LXXX, eighty; DC, six hundred.

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

Thus, V represents five; V, five thousand; LXX represents seventy; LXX, seventy thousand.

41. Read the following:

XX; XXI; XXXV; XXV; XL; LX; LXX; XIX; LXIX; LXIV; XC; XCIV; XCIX; XLIV; CDXX; CCXXIV; VIII; XIX; MDLIV.

Express the following by Roman Notation:

23, 34, 15, 27, 61, 36, 43, 84, 59, 62, 35, 47, 86, 214, 312, 419, 226, 384, 216, 493, 499, 276.

QUESTIONS FOR REVIEW.

42. What is a unit? What is a number? What is arithmetic? What are figures? What beside figures are used to express numbers? What is notation? What is numeration? What is Arabic notation? Why is it called so? How many figures are employed in this system? What is each figure, except naught, called? What other names has naught? What does ty mean in such words as ninety, etc.? What is the principle relating to expressing numbers by two figures? What does teen in the words thirteen, etc., mean? In reading numbers expressed by two figures, what words are omitted?

What is the principle relating to expressing numbers by three figures? How are such numbers read? Why is the Arabic system of notation called the decimal system? From what is the word decimal derived? What are the general principles of notation? How many orders of units are there in each denomination? What is a period? What are the names of the first five periods? What is the rule for numeration? What is the rule for notation?

In the currency of the United States how many mills make a cent? How many cents make a dime? How many dimes make a dollar? How many cents make a dollar? What is the sign of dollars? Where is it written? How are cents and mills distinguished from dollars? How are the cents expressed if the number is less than ten?

What is Roman notation? What are used in this system to express numbers? What are the principles of this system of notation?

43. 1. How many pens are 2 pens and 4 pens?

2. James spent 4 cents for an orange and 3 cents for apples. How much did he spend for both?

3. Mr. Davis had 3 white horses and 4 bay horses. How many horses had he?

4. Emma knit 3 pairs of gloves for her brothers and 2 pairs for her cousins. How many pairs did she knit?

5. A girl learned 5 songs at school and 3 at home. How many songs did she learn?

6. A market woman sold a boy some apples for 5 cents and some pears for 3 cents. How much did he pay her for both.

7. There were 4 birds' nests on one tree and 2 on another. How many were there on both?

8. James spelled 8 words correctly and misspelled 3 words. How many words were there in his lesson?

9. A house has 3 outside doors and 5 doors on the inside. How many doors are there in the house?

10. There are 5 fingers on each hand.

there on both hands?

How many are

11. Jane read 3 pages of a book in the forenoon and 4 in

the afternoon. How many pages did she read?

12. Samuel had 4 marbles and bought 4 more. How many had he then?