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MISCELLANEOUS QUESTIONS.

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1. How far will a man walk in 1711 hours, provided he goes at the rate of 47 miles an hour?

Ans. 82m. 4fur. 8rd. 1ft. 4in. 2. How much land is there in a field, which is 291 rods square?

Ans. 5A. 1R. 32p. 141ft. 10918in. 3. How much wood in a pile, which is 174 feet long, 7 feet high, and 4 feet wide?

Ans. 4cd. 6617ft. 4. What is the value of 197 barrels of four, at $ 69 a barrel?

Ans. $ 134.15% 5. What is the value of 3761 acres of land, at $ 75% per acre?

Ans. $ 28387.064. 6. What cost 17H quintals of fish, at $4.75 per quintal?

Ans. $ 81.55.105. 7. What cost 167075 pounds of coffee, at 12 cents per pound?

Ans. $ 212.999. 8. What cost 281 tons of Lackawana coal, at $ 114 a ton?

Ans. $ 333.271 9. Bought 37 hogsheads of molasses, at $ 17.62 a hhd.; what was the whole cost?

Ans. $ 655.203 10. What cost 3 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 384 rods wide?

Ans. 33A. 3R. 154p. 12. Bought 15 loads of wood, each containing 113 feet, cord measure. I divide it equally between 9 persons; what does each receive?

Ans. 191 ft. 13. If the transportation of 182 tons of iron cost $ 48.15), what is it

per
ton?

Ans. $2.62 14. If a hhd. of wine cost $ 98%, what is the price of one gallon?

Ans. $ 1.561. 15. If 5 bushels of wheat cost $83; what will ä bushel be worth?

Ans. $ 1.643. 16. What will 11 hogsheads and 171 gallons of wine cost, at 19 cents a gallon?

Ans. $ 140.32. 17. How many bottles, each containing 11 pints, are sufficient for bottling a hhd. of cider? Ans. 288 bottles.

18. I have a shed, which is 181 feet long, 101 feet wide, and 714 feet high; how many cords of wood will it contain?

Ans. 11cd. 12482.in.

square foot ?

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

Ans. $ 4.5235 20. How many cubic feet does a box contain, that is 8 feet long, 51, feet wide, and 3 feet high? Ans. 1462.ft.

21. How many feet of boards will it take to cover a side of a house, which is 461, feet long, and 174 feet high?

Ans. 812 ft. 22. How many feet of boards will it take to make 7 boxes, that shall be 54 feet long, 2 i feet high, 31 feet wide; and how many cubic feet will they contain?

Ans. 52733ft. 28633 cub. ft. 23. A certain room is 12 feet long, ilį feet wide, and 71 feet high; how much will it cost to plaster it, at ”cents per

Ans. $ 13.48. 24. A man has a garden that is 141 rods long, and 104 rods wide; he wishes to have a ditch dug around it, that shall be 3 feet wide and 44 feet deep; what will be the expense if he gives 2 cents per cubic foot?

Ans. $223.764 25. How many bushels of grain will a box contain, which is 147 feet long, 511 feet deep, and 44 feet wide, there being 2150; cubic inches in a bushel? Ans. 29434abush.

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 most. 27. Divide $ 1112 equally between 129 men.

Ans. $ 85. 28. Bought 68 barrels of flour at $ 713 per barrel, what was the amount of the whole?

Ans. $ 5383. 29. What cost 83 acres of land at $42, per acre?

Ans. $ 369.20. 30. How shall four 3's be arranged, that their value shall be nothing?

31. From 7 take 11.

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SECTION XVI.

DECIMAL FRACTIONS.

37 1002

.348 is 348

1000

A DECIMAL Fraction is that whose integer is always divided into 10, 100, 1000, &c. equal parts. Its denominator is always an unit, with as many ciphers annexed, as there are places in the given decimal. There is therefore no need of having the denominator expressed; for the value of the fraction is always known by placing a point before it, at the left hand, called the separatrix. Thus, .5 is tó, .37 is

Ciphers annexed to the right hand of decimals do not increase their value; for .4 or .40 or .400 are decimals having the saine value, each being equal to id or }; but when ciphers are placed on the left hand of a decimal, they decrease the value in a tenfold proportion. Thus .4 is id, or four tenths; but .04 is tôd, 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

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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, 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 thousandths.

Let the following numbers be written in words.

27.86 48.07 15.716 161.3 87.006

86.0007

5.6001 34.1063 15.0016 16.1004

1.000007 5.101016 6.716678 1.631 3.760701

16.300000007 1.315 0.0000001 10.10101 1.000327

SECTION XVII.

ADDITION OF DECIMALS.

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

OPERATION.

23.61 161.5

2.6789 61.111 27.0076 116.71 6151.7671 6544.3846

In this question, it will be perceived, that tenths are written under tenths, hundredths under hundredths, &c.; and that the operation of addition is performed as in addition of whole numbers. We therefore induce the following

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 either of the numbers.

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 and seven and fifteen ten thousandths, fifteen and eight hundredths, and forty-nine ten thousandths, together.

Ans. 307 222.086446. 8. What is the sum of twenty-three million and ten, and 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.

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