8. What cost 28 tons of Lackawana coal, at $112 a ton? Ans. $333.27.

9. Bought 371 hogsheads of molasses, at $ 17.62 a hhd.; Ans. $655.20

what was the whole cost? 10. What cost

of a cord of wood, at $ 5.75 a cord?
Ans. $5.03.

11. What are the contents of a field which is 1394 rods long, and 38 rods wide? Ans. 33A. 3R. 1513p.

12. Bought 15 loads of wood, each containing 113 feet, cord measure. I divide it equally between 9 persons; what does each receive? Ans. 19 ft. 13. If the transportation of 183 tons of iron cost $ 48.154, what is it per ton? Ans. $2.62. 14. If a hhd. of wine cost $987, what is the price of one gallon? Ans. $1.5611. 15. If 5 bushels of wheat cost $83, what will a bushel be worth? Ans. $1.64. 16. What will 11 hogsheads and 17 gallons of wine cost, Ans. $140.323. 12 pints, are suffiAns. 288.

at 193 cents a gallon?

17. How many bottles, each containing cient for bottling a hhd. of cider ? 18. I have a shed which is 18

feet long, 105 feet wide,

and 711 feet high; how many cords of wood will it contain?

Ans. 11cd. 12482ft.

19. What will 67 pounds of tea cost, at 65 cents per lb. ?

Ans. $4.5237 contain, that is 84 Ans. 146 ft.

20. How many cubic feet does a box feet long, 5 feet wide, and 3 feet high? 21. How many feet of boards will it take to cover a side of a house which is 46 feet long and 171⁄2 feet high?

occupy.

Ans. 812ft.

22. Required the number of square feet on the surface of 7 boxes, each of which is 5 feet long, 25 feet high, and 32 feet wide; required also the number of cubic feet they would Ans. 5279ft.; 2862 cubic feet. 23. A certain room is 12 feet long, 114 feet wide, and 71 feet high; how much will it cost to plaster it, at 23 cents per square foot ? Ans. $13.487. rods long, and 10 rods around it, that shall be be the expense, if he Ans. $223.761.

24. A man has a garden that is 14 wide; he wishes to have a ditch dug 3 feet wide and 4 feet deep; what will gives 2 cents per cubic foot?

25. How many bushels of grain wil' a box contain which is

1472 feet long, 511 feet deep, and 4 2150 cubic inches in a bushel ?

feet wide, there being Ans. 29432bu.

26. Which will contain the most, and by how much, a box that is 10 feet long, 8 feet wide, and 6 feet deep, or a cubical one, whose each side measures 8 feet?

Ans. The last contains 32 cubic feet the most. 27. Divide $1112§ equally among 129 men. Ans. $85. 28. Bought 68 barrels of flour, at $711 per barrel; what was the amount of the whole ? Ans. $538. 29. What cost 8 acres of land, at $ 423 per acre?

Ans. $369.20.

30. How shall four 3's be arranged, that their value shall be nothing?

31. I have a room 20 feet long, 15 feet wide, and 81 feet high. This room contains 4 windows, each of which is 5 feet in height and 3 feet in width. There are two doors 7 feet high and 3 feet wide. The mop-boards are of a foot wide. A mason has agreed to plaster this room at 64 cents per square yard; a painter is to lay on the paper at 9 cents per square yard; the paper which I wish to have laid on is 23 feet wide, for which I pay 5 cents per yard. What is the amount of my bill for plastering, for papering, and for paper?

Ans. For plastering, $5.1138; for papering, $ 4.37; for paper, $2.80.

SECTION XXII.

DECIMAL FRACTIONS.

A DECIMAL FRACTION is a fraction whose denominator is a unit with as many ciphers annexed as there are places in the numerator. Thus, 10, 100, Too, &c.

157

1000

The denominator being in all cases formed in this obvious manner, there is no necessity of expressing it, and therefore it is not written; but a point is placed before the first figure of the numerator, to indicate that the figure or figures on the right of the point denote a decimal, and not a whole number. Thus, for we write .5, for 5, .15, &c. This point is called the separatrix.

Ciphers annexed to the right hand of decimals do not increase their value; for .4, and .40, and .400 are decimals having

the same value, each being equal to or ; but when ciphers are placed on the left hand of a decimal, they decrease the value in a tenfold proportion. Thus, .4 is, or four tenths; but .04 is, or four hundredths; and .004 is Too, or four thousandths. The figure next the separatrix is reckoned so many tenths; the next at the right, so many hundredths; the third is so many thousandths; and so on, as may be seen by the following

From this table it is evident, that in decimals, as well as in whole numbers, each figure takes its value by its distance from the place of units.

NOTE. If there be one figure in the decimal, it is so many tenths; if there be two figures, they express so many hundredths; if there be three figures, they are so many thousandths, &c.

NUMERATION OF DECIMAL FRACTIONS.

Let the pupil write the following numbers.

1. Three hundred twenty-five, and seven tenths.
2. Four hundred sixty-five, and fourteen hundredths.
3. Ninety-three, and seven hundredths.

4. Twenty-four, and nine millionths.

5. Two hundred twenty-one, and nine hundred thousandths. 6. Forty-nine thousand, and forty-nine thousandths.

7. Seventy-nine million two thousand, and one hundred five thousandths.

8. Sixty-nine thousand fifteen, and fifteen hundred thousandths.

9. Eighty thousand, and eighty-three ten thousandths.

10. Nine billion nineteen thousand nineteen, and nineteen hundredths.

11. Twenty-seven, and nine hundred twenty-seven thousandths.

12. Forty-nine trillion, and one trillionth.

13. Twenty-one, and one ten thousandth.

14. Eighty-seven thousand, and eighty-seven millionths. 15. Ninety-nine thousand ninety-nine, and nine thousand nine billionths.

16. Seventeen, and one hundred seventeen ten thousandths. 17. Thirty-three, and thirty-three hundredths.

18. Forty-seven thousand, and twenty-nine ten millionths. 19. Fifteen, and four thousand seven hundred thousandths. 20. Eleven thousand, and eleven hundredths.

21. Seventeen, and eighty-one quatrillionths.

22. Nine, and fifty-seven trillionths.

23. Sixty-nine thousand, and three hundred forty-nine thou 'sandths.

Let the following numbers be written in words.

1. Add 23.61 and 161.5 and 2.6789 and 61.111 and 27.0076 and 116.71 and 6151.7671 together.

RULE. Write the numbers under each other according to their value, add as in whole numbers, and point off from the right hand as many places for decimals as there are in that number which contains the greatest number of decimals.

2. Add together the following numbers: 81.61356, 6716.31 413.1678956, 35.14671, 3.1671, 314.6. Ans. 7564.0052656. 3. What is the sum of the following numbers: 1121.6116, 61.87, 46.67, 165.13, 676.167895 ? Ans. 2071.449495. 4. Add 7.61, 637.1, 6516.14, 67.1234, 6.1234, together.

Ans. 7234.0968.

5. Add 21.611, 6888.32, 3.6167, together.

Ans. 6913.5477.

6. Add seventy-three and twenty-nine hundredths, eightyseven and forty-seven thousandths, three thousand and five and one hundred six ten thousandths, twenty-eight and three hundredths, twenty-nine thousand and five thousandths, together. Ans. 32193.3826.

7. Add two hundred nine thousand and forty-six millionths, ninety-eight thousand two hundred seven and fifteen ten thousandths, fifteen and eight hundredths, and forty-nine ten thou sandths, together. Ans. 307222.086446.

8. What is the sum of twenty-three million ten, one thousand and five hundred thousandths, twenty-seven and nineteen millionths, seven and five tenths? Ans. 23001044.500069.

9. Add the following numbers: fifty-nine and fifty-nine thousandths, twenty-five thousand and twenty-five ten thousandths, five and five millionths, two hundred five and five hundredths. Ans. 25269.111505.

10. What is the sum of the following numbers: twenty-five and seven millionths, one hundred forty-five and six hundred forty-three thousandths, one hundred seventy-five and eightynine hundredths, seventeen and three hundred forty-eight hundred thousandths? Ans. 363.536487.

SECTION XXIV.

SUBTRACTION OF DECIMALS.

RULE. — Let the numbers be so written, that the separatrix "of the subtrahend be directly under that of the minuend, subtract as in whole