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eighty-five, and 618 billion, 600 million, 850 thousand and 168 trillionths.

Examples to be written in words, and read by the pupil.

(1.) .5. (2.) .05. (3.) .037. (4.) .1008. (5.) 501.08. (6.) .7108. (7.) .008. (8.) .001001. (9.) 16.16. (10.) 180.018. (11.) 7.00016. (12.) 30175.04. (13.) 301680.45. (14.) 30168.045. (15.) 3016.8045. (16.) 301.68045. (17.) 30.168045. II. (18.) 3.0168045. (19.) .30168045. (20.) 35.000100041. (21.) 10010806.3000010806. (22.) 581006

.00940008607.

NOTE. The teacher will find it a profitable exercise to write on the blackboard a number of figures, example 21st or 22d above, for instance, or a shorter example for beginners, and then, removing the decimal point successively from one place to another, require his pupils to read the figures as pointed, and also to point out the local value of any figure or group of figures, either of the whole numbers or the decimals, which he shall underscore. He should continue this exercise till they can readily read the number, and name the local value of any figure or figures, whatever position the decimal point may оссиру.

13. TO WRITE DECIMALS. Write the decimal as if it were a whole number, and then prefix* as many naughts as may be necessary to reduce it to the proper denomination.

Suppose it is required to write five thousand and eighteen ten millionths. Write 5,018, and as ten millionths (see table) is the seventh place from the decimal point, three naughts must be prefixed: .0005,018.

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EXAMPLES TO BE WRITTEN IN FIGURES.

(1.) Four hundredths. (2.) Four thousandths. (3.) Five ten thousandths. (4.) 6 hundred thousandths. (5.) 8 millionths. (6.) 14 hundredths. (7.) 14 thousandths. (8.) 104 thousandths. (9.) 75 ten thousandths. (10.) 851 ten thousandths. (11.) 1845 hundred thousandths. (12.) 16 hundred thousandths. (13.) 58 millionths. (14.) 2506 millionths. (15.) Three, and eight tenths. (16.) 41,—and 7 hundredths. (17.) 400,-and 17 thousandths. (18.) 4,- and 107 ten thousandths. (19.) Eighty-four thousand and sixteen, — and fiftyfour ten thousandths.f

*PREFIX, means to place before; ANNEX, to place after.
+ For more exampels see page 247.

II. (20.) Five million and forty, -and 97 ten millionths. (21.) Fifty billion, 40 million, 75 thousand and 54, -and 5 thousand and 15 hundred thousandths. (22.) 5 trillion, 90 million, 5 thousand, one hundred, and 16 thousand and 5 hundred millionths. (23.) 84 thousand and sixteen, and threethousand and 24 ten millionths.

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14.* 1. In one unit how many tenths? How many hundredths? Thousandths!

2. In two units how many tenths, &c.? In three units, &c.? 3. In one ten how many units? How many tenths? Hundredths? Thousandths?

6. In two hundred how many tens, &c.?

7. In one tenth how many hundredths? thousandths?

4. In two tens how many units, &c.? In three tens, &c.?

5. In one hundred how many tens? Units? Tenths? Hundredths? Thousandths?

Thousandths? Ten

8. In two tenths how many hundredths, &c.?

9. In one hundredth how many thousandths? Ten thousandths? 10. How many units and tenths in 14 tenths? Ans. 1 unit and 4 tenths. In 87 tenths? In 401 tenths? In 806 tenths?

11. How many units, tenths, and hundredths in 347 hundredths? Ans. 3 units, 4 tenths, and 7 hundredths. In 584 hundredths? In 307 hundredths?

12. In 8516 how many hundreds? Ans. 85 hundreds. How many tens? Ans. 851 tens. How many units? Tenths? Hundredths?

13. In 45.16 how many tens? Units? Tenths? Hundredths? 14. In 156.04 how many hundreds? Tens? Units? Tenths? Hundredths?

15. In .3 how many. hundredths? How many thousandths?

NOTE. Naughts placed to the right hand of decimals do not alter their value; for .3 is equivalent to .30; .35 is equivalent † to .350 or

.3500.

II. 16. In 1701.06 how many hundreds? Tens? Units? Tenths? Hundredths? Thousandths? Ten thousandths? Hundred thousandths? Millionths?

Thousands?

17. In 80416.05807 how many ten thousands? Hundreds? Tens? Units? Tenths? Hundredths? Thousandths? Ten thousandths? Millionths? Ten millionths?

18. Write 850 tens. Ans. 8500. (19.) Write 8057 tens. (20.) 9010 hundreds. (21.) 75 tenths. (22.) 875 tenths.

* Beginners may use the slate in Article 14.
+ EQUIVALENT means of equal value.

(23.) 9045 hundredths. (24.) 1645 ten millionths. (25.) 105617 thousandths.

FEDERAL MONEY. (45.)

15. Federal Money is the national currency * of the United States. Every system of national currency has its unit of measure.

In the United States, the unit is the dollar, which is marked thus, $.

The denominations of Federal money are the eagle, the dollar, the dime, the cent, and the mill. † These denominations increase in a tenfold ratio; that is, 10 mills make one cent; 10 cents make one dime; 10 dimes make one dollar; 10 dollars make one eagle. So that all operations in dollars, cents, and mills, are performed as in whole numbers and decimals. Dollars are written as whole numbers; cents, as so many hundredths, and mills as so many thousandths.. The figures, therefore, at the left of the decimal point, express dollars; the first two at the right of the point express cents, and the third, mills. Thus, $7.08 is read 7 dollars and 8 cents; $100.943 is 100 dollars, 94 cents, and 3 mills.

Read the following Numbers. (1.) $8. (1.) $8. (2.) $16.00. (3.) $25.14. (4.) $168.07. (5.) $1016.08. (6.) $45.001. (7.) $1000.011. (8.) $8049.108._(9.) $10010.101.

Write in Figures-(10.) Twenty dollars. (11.) Eightyseven dollars, 25 cents. (12.) One thousand and seven dollars, and nine cents. (13.) Five dollars and eight mills. (14.) Fifteen dollars, three cents and seven mills. (15.) 1000 dollars, 1 cent and 8 mills. (16.) Thirty thousand and eighteen dollars, six cents and three mills.

QUESTIONS FOR EXAMINATION.

What is arithmetic? What is a unit? What is number? What characters are used in writing numbers? Why are they called digits? What are significant figures? Of how many fundamental operations does arithmetic consist? What is numeration? How are the numbers from 1 to 9 expressed? How are numbers larger than 9 expressed? Give examples. How many figures are combined to express numbers between 9 and one hundred? To express numbers larger than ninetynine and less than one thousand? Give examples. Upon what does the value of any figure when combined with others depend? How is

*The term currency signifies money, or the circulating medium. + The mill is merely nominal; there being no coin of this denomination.

its value increased? How diminished? Give examples. In whole ~numbers, which is the place of units? Of tens? Of hundreds? For what purpose is 0 used? How are numbers containing more than three figures to be divided? What does the first, or right hand period contain? The second? The third? The fourth? The fifth? The sixth? Name the periods above the sixth? What is the rule for reading whole numbers? What is the rule for writing whole numbers in figures? Repeat the table, beginning at units.

If a number be divided into ten equal parts, what is one of the parts called? Give an example. If a single thing be divided into ten equal parts, what is one of the parts called? Two of the parts? Four parts? If one thing be divided into one hundred equal parts, what is one of the parts called? Two of the parts? What part of hundreds are tens? What part of tens are units? Where is each written? What part of units are tenths? Where are tenths written? What part of tenths are hundredths? Where are hundredths written? Where are thousandths written? What are decimals? Why are they so called? What is the decimal point? Where placed? Give examples. Repeat the decimal table, beginning at units. What is the rule for reading decimals? For reading whole numbers and decimals? What is the rule for writing decimals? What is the meaning of prefix? Of annex? How is the value of decimals affected by placing naughts at the right of them?

What is Federal Money? What is the meaning of currency? What is the unit of value in the United States currency? How is it marked? What are the denominations of Federal money? What relations do these denominations bear to each other? How are operations in dollars, cents, and mills performed? How are dollars written? Cents? Mills? What do the figures to the left of the decimal point express? What do those at the right express? Give examples.

16. SECTION II

ADDITION.

ADDITION is the method of finding the sum or amount of two or more numbers.

Operations in arithmetic are often represented by signs. The following are used in addition.

=

Sign of equality; as 100 cents = 1 dollar; which is read, 100 cents are equal to one dollar.

+Sign of addition, or plus sign; as, 15+6=21; which is read, 15 and 6 are 21; or 15 plus 6 is equal to 21.

17. 1. How many are 2+2 3+2? 4+2? 5+2? 6+2? 7+2? 8+2? 9+2? 10+2 it+2?

2. Add 3 to all the numbers from 2 to 50. Thus, 2+3=5; 3+3=6; 4+3=7, &c.

3. Add 4 to all the numbers from 2 to 50.

4. Add 5 in the same manner; and 6; and 7; and 8; and 9.

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5. Repeat every third number from 100 to 200; thus, 100+3= 103; 103+3=106; 106+3=109.

6. Name every fourth number in the same manner.

7. Name every fifth number from 1 to 101. to 202.

Every sixth, from 100

8. Name every seventh number from 201 to 300. Every eighth, from 505 to 600.

The pupil should be exercised in this way till he can add units with facility.

9. How many are 10+10? 20+10? 50+10 60+10? 70+10? 80+10?

30+10? 40+10?

10. How many are 10+20? 20+20? &c. 10+30? 20+30? 30+30? &c. 30+40? &c. 10+50? 20+50? &c.

30+20? 40 -207 10+40? 20 -40? 10+60? 20 -60?

&c.

11. How many are 10+15? Say 10 and 10 are 20, and 5 are 25; therefore, 10 and 15 are 25.

12. How many are 12+14? Say 10 and 10 are 20; 2 and 4 are 6, which added to 20 makes 26; therefore, 12 and 14 are 26. 13+12? 14+13? 15+12? 17+11?

13. How many are 23+11? Ans. 20 and 10 are 30; 3 and I are 4, which added to 30, makes 34; therefore, 23 and 11 are 34. 25+14? 22+17? 34+15? 38+21? 4235 43+24? 4832 5317? 65+15? 70+28?

14. How many are 15+18? Say 10 and 10 are 20; 5 and 8 are 13, which is equal to 10 and 3; 20 and 10 are 30 and 3 are 33; therefore, 15 and 18 are 33. 2836? Say 20 and 30 are 50; 8 and 6 are 14, which is equal to 10 and 4; 50 and 10 are 60, and 4 are 64; therefore, 28 and 36 are 64.

15. In the same way add 18+13; 17+15; 19+18; 23+19; 2817; 3417; 39+18; 44+18; 55+27; 48 +27; 54 +37; 2234; 3428; 39+ 47.

16. James has 46 cents and Charles has 27 cents; how many have

both?

17. John gave 35 cents for an arithmetic and 37 cents for a reader; how much did he give for both?

18. A man spent the first 25 years of his life in the country, and he has lived 38 years in the city; how old is he?

19. A farmer bought 2 cows; for one he gave 48 dollars, and for the other 35 dollars; how much did he give for both?

18. A wood merchant buys of one man 310 cords of wood, of another 264 cords, of another 85 cords, and of another 460 cords. How many cords does he buy in all?

These numbers are larger than those we have been adding, and it is not so easy to add them mentally. We will arrange them under each other, so that the units shall stand in one column, the tens in another, &c.

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