CASE IV.

To find the value of any given decimal in the terms of the integer.

1. What is the value of .790625 £.?

Ans. 19s. 9 d.

As a lower denomination consists of more units than the same value in a higher one, therefore to bring pounds to farthings, we must multiply by the same numbers as in common Reduction.

Hence we deduce the following

RULE.

Multiply the given decimal by that number which it takes of the next denomination to make one of that greater, and cut off as many places for a REMAINDER on the right, as there are places in the given decimal. Multiply the REMAINDER by the next lower denomination, and cut off for a remainder as before, and so proceed, until the decimal is reduced to the denomination required; the several denominations, standing at the left hand, are the answers required.

Ans. 3R. 30p. 13ft. 9 in.

7. Reduce .5615 of a hogshead of wine to its value in gallons,

& C.
8. Reduce .367 of a year to its value in days, &c.

Ans. 35 gal. 1qt. Opt. 3123gi.

1250

Ans. 184da. 1h. 7m. 19 sec.

9. What is the value of .6923828125 of a cwt. ?

Ans. 2qr. 21lb. 8oz. 12dr.

10. What is the value of .015625 of a bushel?

11. What is the value of .55 of an ell English?

12. What is the value of .6 of an acre ?

Ans. 1 pint.

Ans. 2qr. 3na.
Ans. 2R. 16p

SECTION XXII.

MISCELLANEOUS EXAMPLES.

28

1. What is the value of 7cwt. 2qr. 18lb. of sugar, at $11.75 per cwt.? Ans. $90.01.3. 2. What cost 19cwt. 3qr. 14lb. of iron, at $9.25 per cwt.? Ans. $183.84.3.

3. What cost 39A. 2R. 15p. of land, at $ 87.37.5 per acre?

Ans. $3459.50.322.

Ans. $50595.414.

4. What would be the expense of making a turnpike 87m. 3fur. 15rds., at $578.75 per mile? 5. What is the cost of a board 18ft. 9in. long, and 2ft. 3 in. wide, at $.05.3 per foot? Ans. $2.27.7.

6. Goliah of Gath was 6 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 29 miles? Ans. 6h. 50m. 6sec.+ 8. What is the cost of 5yd. 1qr. 2na. of broadcloth, at $ 5.625 per yard? Ans. $30.23.48. 9. Bought 17 bags of hops, each weighing 4cwt. 3qr. 7lb., at $5.87 per cwt.; what was the cost? Ans. $480.64.87. 10. Purchased a farm, containing 176A. 3R. 25rds., at $75.37) per acre: what did it cost? Ans. $13334.30.819.

11. What cost 17625 feet of boards, at $12.75 per thousand ? Ans. $224.71.83. 12. How many square feet in a floor 19ft. Sin. 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?

Åns. 524yd.

14. How many solid feet in a pile of wood 10ft. 7in. long, 4ft. wide, and 5ft. 10in. high? Ans. 246 ft.

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

Ans. 24.

16. Bought 1gal. 2qt. 1pt. of wine for $1.82; what would be the price of a hogshead? Ans. $70.56.

17. Bought 1254yd. 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 cwt.?

Ans. $634.56.2.

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

Ans. $675.84.

20. How many solid feet in a stick of timber 34ft. 9in. long,

1ft. Sin. wide, and 1ft. 6in. deep?

Ans. 65.15625ft.

21. How many cwt. of coffee in 173 bags, each bag containing 2cwt. 1qr. 71b. ? Ans. 41cwt. Oqr. 54lb. 22. If 18yd. 1qr. of cloth cost $36.50, what is the price of 1 yard? Ans. $2.00. 23. If $477.72 be equally divided between 9 men, what will be each man's share? Ans. $53.08. 24. A man bought a barrel of flour for $ 5.37.5, 7gal. of molasses for $1.78, 9 gal. of vinegar for $1.1875, 1 gal. of wine for $1.125, 14lb. of sugar for $1.275, and 5lb. of tea, for $2.625 ; what did the whole amount to? Ans. $13.36.7. 25. A man purchased 3 loads of hay; the first contained 2} tons, the second 3 tons, and the third 1 tons; what was the value of the whole, at $ 17.625 a ton ? Ans. $128.88.213. 26. At $13.625 per cwt., what cost 3cwt. 2qr. 7lb. of sugar? Ans. $48.53.91. 3R. 35rds. ?

27. At $125.75 per acre, what cost 37A.

Ans. $4774.57.0

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

Ans. $198.98.4§.

29. What cost 7 bales of cotton, each weighing 3.37cwt., at $9.37 per cwt. ? Ans. $244.85.19. 30. What cost 7hhd. 49gal. of wine, at $97.625 per hhd.? Ans. $759.30.535.

63

31. What cost 7yd. 3qr. 3na. of cloth, at $ 4.75 per yard? Ans. $37.70.3}. 32. What cost 27T. 15cwt. 1qr. 34lb. of hemp, at $183.62 per ton ? Ans. $5098.03.7 33. What is the cost of constructing a railroad 17m. 3fur. 15rd., at $ 1725.87.5 per mile? Ans. $30067.97.833.

SECTION XXIII.

EXCHANGE OF CURRENCIES.

PREVIOUS to the year 1776, all accounts in this country were kept in pounds, shillings, pence, and farthings; but owing to the depreciation of the currency, a dollar was estimated differently in different countries.

In New England, Virginia, Kentucky, Tennessee, and Ohio, the dollar is valued at

6s. Od.

New York, North Carolina, and New Jersey,

8s. Od.

Pennsylvania, Delaware, and Maryland,

7s. 6d.

South Carolina and Georgia,

4s. 8d.

Canada and Nova Scotia,

5s. Od.

England and Newfoundland (sterling),

4s. 6d.

In order, therefore, to change any of the above currencies to federal money, the shillings, pence and farthings, if there be any, must first be reduced to decimals of a pound, and annexed to the pounds. We then adopt this general

RULE.

Divide the pounds by the value of a dollar in the given currency, EXPRESSED BY A FRACTION OF A POUND; that is, to change the old New England currency to federal money, divide by because 6 shillings is of a pound.

To change the old currency of New York, &c., to federal money, divide by ; because 8 shillings is of a pound.

To change the old currency of Pennsylvania, &c., to federal money, divide by ; because 7 shillings and 6 pence is of a pound.

To change the old currency of South Carolina and Georgia to federal money, divide by; because 4 shillings and 8 pence of a pound.

is

To change Canada and Nova Scotia currency to federal money, divide by ; because 5 shillings is of a pound.

To change English (sterling) money to federal money, divide by; because 4 shillings and 6 pence is of a pound.

To change sterling money to lawful money, add to the sterling, and the sum will be the lawful; because 4 shillings and 6 pence sterling is 6 shillings lawful; and, for the same reason, take from the lawful, and the remainder will be sterling.

To reduce federal money to any of the above currencies, the federal money must be MULTIPLIED by the above fractions.

EXAMPLES.

1. Change 18£. 4s. 6d. of the old New England currency to federal money.

18.225£. $60.75 Answer.

In this example we reduce the 4 shillings and 6 pence to a decimal of a pound, which we find to be .225. This decimal we annex to the pounds, and multiply the 18.225£. by 10, and divide by 3, and it produces the answer $ 60.75. The reason for this process has already been shown.

2. Change $ 60.75 to the old currency of New England.

$60.75X18.225-18£. 5s. 6d.

= Answer.

The decimal .225 is reduced to shillings and pence by Case IV. of Decimal Fractions.

3. Change 78£. 7s. 6d. of the old currency of New England to federal money.

Ans. $261.25.

4. Change $261.25 to the old currency of New England. Ans. 78£. 7s. 6d.

5. Change 46£. 16s. 6d. of the old currency of New York to federal money. Ans. $117.06. 6. Change $117.064 to the old currency of New York.

Ans. 46£. 16s. 6d.

7. Change 387£. of the old currency of New Jersey and Pennsylvania to federal money. Ans. $1032. 8. Change $1032 to the old currency of New Jersey and Pennsylvania.

Ans. 387 £.

9. Change 12£. 12s. of the old currency of South Carolina and Georgia to federal money.

Ans. $54.

10. Change $54 to the old currency of South Carolina and Georgia. Ans. 12£. 12s. 11. Change 128£. 18s. 6d. of Canada and Nova Scotia to federal money. 12. Change $515.70 to Canada and Nova Scotia currency. Ans. 128£. 18s. 6d.

Ans. $515.70.

13. Change 162£. 18s. English money (sterling) to federal money.

14. Change $724 to sterling money.
15. Change 347 £. sterling to lawful money.

Ans. $724. Ans. 162£. 18s.

Ans. 462£. 13s. 4d.
Ans. 347 £.

16. Change 462£. 13s. 4d. lawful to sterling.

SECTION XXIV.

CIRCULATING DECIMALS. *

DEFINITIONS.

1. Those decimals that are produced from Vulgar Fractions, whose denominators do not measure their numerators, and are distinguished by the continual repetition of the same figure or figures, are called infinite decimals.

2. The circulating figures, that is, those that continually repeat, are called repetends; and, if the same figure only repeats, it is called a single repetend; as .11111 or .5555, and is expressed by writing the círculating figure with a point over it; thus, .11111, and is denoted by .i, and .5555 by .5.

*As Circulating Decimals are not so much of a practical nature as many other rules, and as they are somewhat difficult in their operation, the student can omit them until he reviews arithmetic.