16. Divide six hundred seventy-eight thousand seven hundred sixty-seven millionths by three hundred twentyeight thousandths. Ans. 2.069.

Section 31.

REDUCTION OF DECIMALS.

I. To reduce a vulgar fraction to a decimal.

1. Reduce ğ to a decimal.

OPERATION.

8) 5.000
.625

That the decimal .625 is equal to §, may be shown by writing it in a vulgar fraction and reducing it thus,

Ans.

625

=

NOTE. It is also evident, that .625 is equal to §, because the numerators have equal ratios to their denominators.

Hence the following

RULE.

Divide the numerator by the denominator, annexing one or more ciphers to the numerator, and the quotient will be the decimal required.

NOTE. It is not usually necessary, that decimals should be carried to more than six places.

2. Reduce to a decimal.

3. Reduce to a decimal.

Ans. .75.

Ans. .875.

4. What decimal fraction is equal to ? Ans. .4375.

5. Reduce to a decimal.

6. Reduce to a decimal.

Ans. .363636+.
Ans. .416666+.

II. Reduce compound numbers to decimals.

7. Reduce 8s. 6d. 3qr. to the decimal of a £.

Write the given numbers perpendicularly under each other for dividends, proceeding orderly from the least to the greatest; opposite to each dividend on the LEFT hand, place such a number for a divisor, as will bring it to the next superior name, and draw a line between them. Begin at the highest, and write the quotient of each division, as decimal parts, on the RIGHT of the dividend next below it, and so on, until they are all divided; and the last quotient will be the decimal required.

8. Reduce 15s. 6d. to the fraction of a £. Ans. .775. 9. Reduce 5cwt. 2qr. 14lb. to the decimal of a ton.

Ans. .28125.

10. Reduce 3qr. 21lb. to the decimal of a cwt.

Ans. .9375.

11. Reduce 6fur. 8rd. to the decimal of a mile.

Ans. .775.

12. Reduce 3R. 19p. 167ft. 72in. to the decimal of an Ans. .872595+.

acre.

NOTE 1. If it be required to reduce pounds, shillings, pence, and farthings, of the old New England currency, to dollars, cents, and mills; the pounds, shillings, &c. may be reduced to the decimal of a £; and if this decimal be multiplied by 10 and the product divided by 3, the quotient will be dollars and cents. But if the above decimal be multiplied by 10, and the product be divided by 4, the quotient will be the reduction of the old currency of New York to dollars and

cents.

NOTE 2. If it be required to bring English sterling money to dollars and cents, let the pounds, &c. be reduced to the decimal of a penny; then divide this decimal by and the quotient is dollars

and cents.

13. Change 18£. 15s. 6d. of the old New England currency, to dollars and cents.

OPERATION.

18£. 15s. 6d. 18.775£.; 18.775 × 40 = $62.58 Ans.

=

14. Change 15£. 15s. 9d. of the old currency of New York, to dollars and cents.

OPERATION.

15£. 15s. 9d.=15.7875£.; 15.7875×4=$39.46.82 Ans.

15. Change 176£. 19s. 9d. sterling to United States currency. Ans. $786.61 +.

OPERATION.

176£. 19s. 9d. =176.9875£.; 176.9876x=$786.61 +.

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

16. What is the value of .9875£. ?

OPERATION.

$9875 20 19.7500

12

9.0000

Hence the following

Ans. 19s. 9d.

This question is performed by the same principle we adopted in finding the value of a vulgar fraction in the known parts of the integer.

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 hand, 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.

1. What is the value of .628125 of a £?

Ans. 12s. 6d.

2. What is the value of .778125 of a ton ?

Ans. 15cwt. 2qr. 7lb.

3. What is the value of .75 of an ell English?

Ans. 3qr. 3na.

4. What is the value of .965625 of a mile ?

Ans. 7fur. 29rd.

5. What is the value of .94375 of an acre?

Ans. 3R. 31p.

6. What is the value of .815625 of a pound Troy ?

Ans. 9oz. 15dwt. 18gr.

7. What is the value of .5555 of a pound apothecary's weight? Ans. 63. 53. 09. 191gr.

Section 32.

EXERCISES IN DECIMALS.

1. What is the value of 15cwt. 3qr. 14lb. of coffee at

$9.50 per cwt. ?

2. What cost 17T. 18cwt. 1qr. 7lb. per ton?

3. What cost 37A. 3R. 16p. of acre?

4. What cost 15yd. 3qr. 2na. of yard?

5. What cost 15g cords of wood at

6. What cost the construction of
railroad at $3765.60 per mile ?
7. What cost 27hhd. 21gal. of
$15.37 per hogshead?

Ans. $150.81+. of potash at $53.80 Ans. $963.86+. land at $75.16 per Ans. $2844.80+. cloth at $3.75 per

Ans. $59.53+. $4.62 per cord?

Ans. $71.10. 17m. 6fur. 36rd. of Ans. $67263.03+. temperance wine at Ans. $420.24+.

8. What are the contents of a pile of wood, 18ft. 9in. long, 4ft. 6in. wide, and 7ft. 3in. high?

Ans. 611ft. 1242in. 9. What are the contents of a board 12ft. 6in. long, and 2ft. 9in wide? Ans. 34ft. 54in. 10. Bought a cask of vinegar containing 25gal. 3qt. 1pt. at $0.37 per gallon; what was the amount? Ans. $9.70+. 11. Bought a farm containing 144A. 3R. 30p. at $97.62} per acre; what was the cost of the farm? Ans. $14149.52+.

12. Sold Joseph Punson 3T. 18cwt. 21lb. of salt hay, at $9.37 per ton. He having paid me $20.25, what remains due ? Ans. $16.40+. 13. If of a cord of wood cost $5.50, what cost one cord? What cost 7 cords?

Ans. $48.71+.

Section 33.

SIMPLE INTEREST.

INTEREST is the compensation, which the borrower of money makes to the lender.

PRINCIPAL is the sum lent.

AMOUNT is the interest added to the principal.

PER CENT., a contraction of per centum, is the rate established by law, or that which is agreed on by the parties, and is so much for a hundred dollars for one

year.

GENERAL RULE.

Let the per cent. be considered as a decimal of a hundred dollars, and multiply the principal by it, and the product is the interest for one year; but, if it be required to find the interest for more than one year, multiply the product by the number of years.

NOTE. The decimal for 6 per cent. is .06; for 7 per cent. .07; for 8 per cent. .08; for 94 per cent. .0925; for 2 per cent. .025, &c. The decimals must be pointed off as in Multiplication of Decimal Fractions.

This rule is obvious from the fact, that the rate per cent. is such a part of every hundred dollars. Thus, 6 per cent. is of the principal.

NOTE. When no particular per cent. is named, 6 per cent. is to be understood, as it is the legal interest in the New England States generally. In New York the legal interest is 7 per cent.