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Contracted way. 92.41035)2508.928065051(27.1498 1848 207

Common way. 92.41035)2508.928065051(27.1498 660721

1848 2070 646872

66072106 13849

64687245 9241

13848615 4608

9241035 3696

4607 5800 912

36964140 832

91116605 80,

83169315
72

79472901
73928280

5544621 2. Divide 721.17562 by 2.257432, and let there be only 3 places of decimals in the quotient. Quo. 319.467

3. Divide 12.169825 by 3.14169, so as to have 5 places of decimals in the quotient.

Quo. 3.87377

REDUCTION OF DECIMAL:S.

CASE 1.
To reduce a vulgar fraction to a decimal.

RULE. Annex as many ciphers to the numerator as may be necessary, and divide it by the denominator.

Note. –There must be as many decimal places in the quotient as there are ciphers annexed to the numerator.

When a compound fraction is given, first reduce it to alsingle one, and then to a decimal.

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To reduce any sum, or quantity, to the decimal of any given denomination.

RULE. Divide the given sum or quantity, reduced to the lowest denomination mentioned, by the proposed integer, reduced to the same denomination, and the quotient will be the decimal required. Or,

Write the given numbers froin the least to the greatest in a perpendicular column, and divide each of them by such a number as will reduce it to the next denomination, annexing the quotient to the succeeding number; the last quotient will be the decimal required.

EXAMPLES. 1. Reduce :175. 6d. to the decimal of a pound. d. d.

240.)210.000(.875 decimals. 17 6 = 210

1920 IL 3 240

1800

1680
12 6.0
210 | 17:5010

1200

1200 .875 decimal. 2. Reduce 7s. 6d. to the decimal of a pound.

Result .375 3. Reduce 9d. to the decimal of a pound. Result .0375

Or thus,

a

a

4. Reduce 10s. 92d. to the decimal of a pound.

Result .5385416+ 5. Reduce 12 grains to the decimal of a lb. troy.

Result .002083 6. Reduce 12 drams to the decimal of a lb. avoirdupois.

Result .046875 7. Reduce 2 qrs. 14 Ib. to the decimal of a cwt.

Result .625 8. Reduce 2 furlongs to the decimal of a league.

Result .0833 9. Keduce 3 qrs. 2 na. to the decimal of a yard.

Result .875 10. Reduce 4 perches to the decimal of an acre.

Result .025 11. Reduce 1 pint to the decimal of a gallon.

Result .125 12. Reduce 7 minutes to the decimal of a day.

Result .00480+ 13. Reduce 72 days to the decimal of a year, computing the year at 365 days.

Result .1972602+ 14. Reduce 52 days to the decimal of a year, computing the year at 3651 days.

Result .142368 + 15. Reduce d. to the decimal of a shilling.

Result .0625

a

CASE 3.
To reduce a decimal fraction to its value.

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RULE. Multiply it by the known parts of the integer, and separate to the right of the product as many places as there are places in the given number.

Nate.To find the value of any decimal of a pound by inspection, double the first figure after the point for shillings, adding one thereto if the second be five or more:

Prefix the second figure, if less than five, or its excess, above five to the third, and call them so many farthings, abating one when above 12, and 2 when above 36.

EXAMPLES 1. What is the value of .87615 of a L.? Ans. 175. 61d. .87615

By inspection. 20

.87615

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1.10400 2. What is the value of .7854166 of a L.?

Ans. 15s. 8 d. 3. What is the value of .76 of a L.?

Ans. 15 s., 2 d. 1.6 qrs. 4. What is the value of .625 of a shilling? Ans. 7d. 5. What is the value of ,461 of a dollar ?

Ans. 46 cts. I mill. 6. What is the value of .461 of a shilling?

Ans. 5d. 2.128 qrs. 7. What is the value of .86 of a cwt. ?

Ans. 3 qrs. 12 lb. 5 oz. 1.92 dr. 8. What is the value of .7 of a lb. troy?

Ans. 8 oz. 8 dwt. 9. What is the value of .71 of 4 oz. troy ?

Ans. 2 oz. 16 dwt. 19.2 grs, 10. What is the value of .761 of a day?

Ans. 18 h. 15 min. 50.4 sec. il. What is the value of .67 of a league?

Ans. 2 miles, o fur. 3 poles, lyd. 3.6 in. 12. What is the value of .712 of a furlong?

Ans. 28 poles, 2 yds. 1 ft. 11.04 in. 13. What is the value of .6875 of a yard?

Ans. 2 qrs. 3 na. 14. What is the value of .3375 of an acre ?

Ans. I rood, 14 perches. 15. What is the value of .3 of a year?

Ans. 109.days, 12 hours.

a

a

16. What is the value of .07 of a barrel of 32 gallons ?

Ans. 2 gals. 1.92 pts. 17. What is the sum of .48 of a pound, and .16 of a shilling?

Ans. 9s. 9.12d. 18. What is the sum of 17 of a lb. troy, and .84 of an ounce ?

Ans. 2.oz. 17 dwt. 14.4 grs. 19. What is the difference between .17 L, and 7s.?

Ans. 25. 8 d. 1.6 qr. 20. What is the difference between .41 day and .16 hour?

Ans. 9 h. 40 min. 48 sec.

THE SINGLE RULE OF THREE DIRECT,

IN DECIMALS.

L. S.

L.

8, d.

The operation both in direct and inverse proportion is the same as in whole numbers, regard being had to the right placing of the points.

EXAMPLES. 1. If 2.75 yards of cloth cost 4 L. 13.5s. what are 12.25 yards worth?

Ans. 20L. 16s, 6d. vds.

yds. As 2.75 : 4 13.5 :: 12.25 : 20 16 6 2. If 1.4 lb, of mace cost 14.5s. what cost 75.31 lb.

Ans. 38 L. 19s. Ild. 3.52 qrs. 3. If 1.5 oz. of silver be worth 7.88. what is the value of 9.7 lb.?

Ans. 30 L. 58. 3d. 1.44 qrş. 4. If 1.47 cwt. of sugar be worth 4.5 L. how much is 1.7 lb. worth?

Ans. 11.1d. 5. If 1.6 cwt. of sugar sell for 3 L. 12.76s. what is the value of 3 hogsheads, each 11 cwt. 3 qrs. 10.12 lb.

Ans. 30L. 15s. 3d. 3.36 qrs. 6. What is the value of 3 pieces of cloth, each containing 21.5 ydş. at 12.35. per yard? Ans. 39 L. 133. 4.2d. 7. If I pint of wine cost 1.2s. what cost 12.5 hogsheads?

Ans. 378 L, 8. If 19 yards of linen cost 25.75 dols. what will 435.5 yards come to?

Ans. 590.217 dols.+ Or,

590 dols. 21 ctş. 7m. to

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