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750000 we multiply by 4, and pointing off have 3 farthings, which, taken with the other denominations obtained, gives 15s. 9d. 3far. for the answer.

RULE. Multiply the decimal by that number which will reduce it to the next lower denomination, and point off as in multiplication of decimals.

Then, multiply the decimal part of the product, and point off as before. So continue till the decimal is reduced to the denominations required.

The several whole numbers of the successive products will be the

answer.

NOTE. — When there is a decimal in the last product, it may be changed to a common fraction.

EXAMPLES.

Ans. 7d.

2. What is the value of .625 of a shilling ? 3. What is the value of .6725 of a cwt. ?

Ans. 2qr. 171b. 4oz. 4. What is the value of .9375 of a yard ? 5. What is the value of .7895 of a mile ?

Ans. 6fur. 12rd. 10ft. 62 in. 6. What is the value of .9378 of an acre ?

Ans. 3R. 30p. 13ft. 999 in. 7. Reduce .5615 of a hogshead of wine to its value in gallons, &c.

Ans. 35gal. 1qt. Opt. 313 gi. 8. Reduce .367 of a year to its value in days, &c.

Ans. 134d. 1h. 7m. 19 sec. 9. What is the value of .6923828125 of a cwt. ?

Ans. 2qr. 191b. 3oz. 13d. 10. What is the value of .015625 of a bushel ? 11. What is the value of .55 of an ell English ?

Ans. 2qr. 3na. 12. What is the value of .6 of an acre ? Ans. 2R. 16p.

MISCELLANEOUS EXAMPLES.

per cwt. ?

1. What is the value of 7cwt. 2qr. 18lb. of sugar, at $ 11.75

Ans. $ 90.24. 2. What cost 19cwt. 3qr. 141b. of iron, at $ 9.25 per

cwt. ?

3. What cost 39A. 2R. 15p. of land, at $87.375 per acre ?

Ans. $ 3459.50343. 4. What would be the expense of making a turnpike 87m. 3fur. 15rd., at $ 578.75 per mile ? Ans. $50595.41&t.

5. What is the cost of a board 18ft. 9in. long, and 2ft. 3fin. wide, at $.053

per
foot ?

Ans. $ 2.27741. 6. Goliath of Gath was 62 cubits high; what was his height in feet, the cubit being 1ft. 7.168in. ? Ans. 10ft. 4.592in.

7. If a man travel 4.316 miles in an hour, how long would he be in travelling from Bradford to Boston, the distance being 294 miles ?

Ans. 6h. 50m. 6sec. + 8. What is the cost of 5yd. lqr. 2na. of broadcloth, at $ 5.624 per yard ?

Ans. $ 30.2343. 9. Bought 17 bags of hops, each weighing 4cwt. 3qr. 71b., at $ 5.874 per cwt. ; what was the cost ?

10. Purchased a farm, containing 176A. 3R. 25rd., at $ 75.374 per acre; what did it cost? Ans. $ 13334.308}}.

11. What cost 17625 feet of boards, at $ 12.75 per thousand ?

Ans. $ 224.7187. 12. How many square feet in a floor 19ft. 3in. long, and 15ft. 9in. wide ?

Ans. 303ft. 27in. 13. How many square yards of paper will it take to cover a room 14ft. 6in. long, 12ft. 6in. wide, and 8ft. 9in. high? 14. How

many solid feet in a pile of wood 10ft. 7in. long, 4ft. wide, and 5ft. 10in. high ?

Ans. 2461&ft. 15. How many garments, each containing 4yd. 2qr. 3na., can be made from 112yd. 2qr. of cloth ?

16. Bought Igal. 2qt. lpt. of wine for $ 1.82 ; what would be the price of a hogshead ?

Ans. $ 70.56. 17. Bought 125£yd. of lace for $15.06; what was the price of 1 yard?

Ans. $ 0.12. 18. What cost 17cwt. 3qr. of wool, at $ 35.75 per hundredweight?

Ans. $ 634.562. 19. What cost 7hhd. 47 gal. of wine, at $ 87.25 per hogshead?

Ans. $ 675.84 20. How many solid feet in a stick of timber 34ft. Iin. long, 1ft. 3in. wide, and ift. 6in. deep?

Ans. 65.15625ft. 21. If 18yd. lqr. of cloth cost $ 36.50, what is the price of 1 yard?

Ans. $ 2.00.

8

sugar?

22. If $ 477.72 be equally divided among 9 men, what will be each man's share ?

Ans. $ 53.08. 23. A man bought a barrel of flour for $ 5.375, 7gal. of molasses for $ 1.78, 9gal. of vinegar for $ 1.1875, lgal. of wine for $ 1.125, 1 tlb. of sugar for $ 1.275, and 5lb. of tea for $ 2.625; what did the whole amount to?

Ans. $13.3674. 24. A man purchased 3 loads of hay; the first contained 23 tons, the second 33 tons, and the third 1 16 tons; what was the value of the whole, at $ 17.625 a ton ? Ans. $ 128.88214.

25. How many hogsheads of water will it take to fill a cistern which is 15.25 feet long, 8.4 feet wide, and 10 feet deep?

Ans. 152hhd. 6 Agal. 26. At $ 13.625 per cwt., what cost 3cwt. 2qr. 7lb. of

Ans. $ 48.6411. 27. At $ 125.75 per acre, what cost 37A. 3R. 35rd. ?

Ans. $ 4774.570 P6 28. At $ 11.25 per cwt., what cost 17cwt. 2qr. 21lb. of rice?

Ans. $199.2371. 29. What cost 74 bales of cotton, each weighing 3.37cwt., at $ 9.374 per cwt.?

30. What cost 7hhd. 49gal. of wine, at $ 97.625 per hogshead ?

Ans. $ 759.3053. 31. What cost 7yd. 3qr. 3na. of cloth, at $4.75 per yard?

Ans. $ 37.7035. 32. What cost 27T. 15cwt. lqr. 3;lb. of hemp, at $ 183.62

Ans. $ 5098.071117. 33. What is the cost of constructing a railroad 17m. 3fur. 15rd., at $ 1725.875

per

mile ? Ans. $ 30067.97834. 34. When $ 624.53125 are paid for 17A. 3R. 15p. of land, what is the cost of one acre ?

35. Paid $ 494.53125 for 19T. 15cwt. 2qr. 14lb. of hay; what was the cost per ton ?

Ans. $24.999329 36. How much land, at $ 40 per acre, can be obtained for $ 1004.75 ?

Ans. 25A. OR. 19p. 37. How many cords of wood can be put into a space 20.5 feet long, 12.75 feet wide, and 7.6 feet high?

Ans. 15 cords 66% cubic feet. 38. How many bushels of corn at $ 0.62, per bushel must a farmer exchange for 31 yards of sheeting at $ 0.08per yard, and 74 yards of broadcloth at $ 2.75 per yard ? Ans. 3740

per ton ?

39. I have expended $ 42.875 for a quantity of grain, 1% of it being corn, at $ 0.75 a bushel ; io of it wheat, at $ 2 a bushel; and the balance oats, at $ 0.40 a bushel, to the amount of $ 3.50. Required the number of bushels of each kind purchased.

40. If a mason, in constructing a drain 250.35 feet long, begin with a width of 8 inches, and increase o of an inch in every foot of length, how many times the width of the beginning of the drain will its end be? Ans. 16.646875.

41. A gentlenian gave of his property to his son James ; } of it to his son William; } of the remainder to his daughter Mary; and the balance to his wife. It appeared that Mary received $ 2243.26 less than James. What was the amount divided, and how much did each receive ? Ans. Amount, $ 13459.56; James, $ 3364.89; William,

$ 4486.52; Mary, 1121.63 ; 'wife, $ 4486.52.

CIRCULATING DECIMALS.

281. A CIRCULATING DECIMAL is a decimal in which one or more figures are continually repeated in the same order. Thus, in reducing $ to an equivalent decimal, on annexing ciphers and dividing by the denominator, the result obtained, .333+, is a circulating decimal; for, however far the division might be carried, the same figure would continue to be repeated without the decimal terminating.

Such decimals are sometimes called infinite, or repeating; and, for sake of distinguishing, those decimals that terminate are sometimes termed finite.

282. A repetend is a figure, or a series of figures, continually repeated. To mark a repetend, a point (.) is placed over a single repeating figure, or over the first and last of a series of repeating figures. Thus, in .3, the point denotes that the 3 is a repetend; and in 72, that the 72 is a repetend. 283. A single repetend is one in which only one figure is

or

repeated; as in .1111+ denoted by .i ; and 2222 +, denoted by 2.

284. A compound repetend is one in which the same set of figures is repeated; as in .135135t, denoted by .135, and .30363036+, denoted by 3036.

285. A pure repetend is one which contains only the figures of the repetend; as, ., .02, and .i23.

286. A mixed repetend is one in which a repetend is preceded in the same fraction by one more figures. The figures preceding the repetend are called the finite part. Thus, .416 is a mixed repetend, of which the figure 6 is the repetend, and the figures 41 the finite part; also, 1.728 is a mixed repetend, of which the figures 28 are the repetend, and the figures 1.7 the finite part.

287. A perfect repetend is a pure repetend containing the same number of figures as there are units in its denominator less one. Thus, + reduced to a decimal gives .142857, which, as it contains as many figures as there are units in the denominator, 7, less one, is a perfect repetend.

288. Similar repetends are those which begin at the same distance from the decimal point ; as .3 and .0; or 5.123 and 3.478.

289. Dissimilar repetends are those which begin at different distances from the decimal point; as .986 and .4625 ; or .5925 and .0423436.

Conterminous repetends are those which terminate at the same distance from the decimal point; as .63i and.463, or .0753 and .4752.

291. Similar and conterminous repetends are those which both begin and end at the same distance from the decimal point; as .354 and .423; or .5757 and 5723.

292. Repetends always arise from common fractions, which, when in their lowest terms, contain in their denominator other factors than 2 and 5. For when a common fraction is in its lowest terms, its numerator and denominator are prime to each

290.

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