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The foot being equal to 12 inches, the vulgar fraction will be "s; then 12)9.00 .75 = decimal fracstion required. Reduce 8 inches the decimal of a yard. * 8 inches

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Reduce 5 furlongs 12 perches to the dicinal of a mile.

1 mile 5 furlongs, 8 40 8 fur. 200 40 —=vulgar fraction. * 320 320 per. 320)2000(.625 = decimal sought. 1920 ... . 800 640 1600 1600

Reduce 21 minutes 54 seconds to the decimal of a degree. Ans. .365

Reduce 056 of a pole to the decimal of an Acre. Ans. .00035

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Reduce 13 cents to the decimal of an Eagle.
Ans. .013 -
Reduce 14 minutes to the decimal of a day.
Ans. .00972+ /
Reduce 3 hours 46 minutes to the decimal of a
week. Ans. .0224206+

RULE III.

To find the value of Decimal Fractions in terms of the lonyer denominations.

Multiply the given decimal by the number of the next lower denomination, which makes an integer of the present, and point off as many places at the right hand of the product, for a remainder, as there are figures in the given decimal. Multiply this remainder by the number of the next inferior denomination, and point off a remainder, as before. Proceed in this manner through all the parts of the integer, and the several denominations, standing on the left hand, are the value required.

EXAMPLES.

Required the value of .3375 of an acre. 4 = number of roods [in an acre.

1.3500
40 = number of perch-
ses in a rood.

... 14.0000 The value, therefore, is 1 rood 14 perches.

/

What is the value of .6875 of a yard? 3=number of feet in a [yard.

2.0625
12=number of inches in
[a foot.

.7500
12=number of lines in
o |an inch.

- 9.0000
The answer here is 2 feet 9 lines.

What is the value of .084 of a furlong? Ans. 3 per. I yd. 2 ft. II in. What is the value of 683 of a degree? Ans. 4 m. 58 sec. 48 thirds. ~ What is the value of .0053 of a mile? Ans. I per. 3 yds. 2 ft. 5 in...+ What is the value of .036 of a day ? Ans. 51’ 50" 24". - PROPORTION IN DECIMAL FRACTIONS.

Having reduced all the fractional parts in the given quantities to their corresponding decimals, and having stated the three known terms, so that the fourth, or required quantity, may be as much greater, or less than the third, as the second term is greater, or less than the first, then multiply the second and third terms together, and divide the product by the first term, and the quotient will be the answer;-in the same denomination with the third term.

EXAMPLES.

if 3 acres 3 roods of land can be purchased for 93 dollars 60 cts. how much will 15 acres 1 rood cost at that rate

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If a clock gain 14 seconds in 5 days 6 hours, how much will it gain in 17 days 15 hours? Ans. 47 seconds. *

lf 187 dollars 85 eents gain 12 dollars 33 cents

interest in a year, at what rate per cent is this interest? Ans. 6.56+

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INvoluTION is the method of raising any number, considered as the root, to any required power. Any number, whether given, or assumed at . pleasure, may be called the root, or first power of this number; and its other powers are the pro

ducts, that result from multiplying the number

by itself, and the last product by the same number again; and so on to any number of multiplications.

The index, or exponent, is the number denoting the height, or degree of the power, bein always greater by one, than the number of multiplications employed in producing the power. It is usually written above the root, as in the following ExAMPLE, where the method of involution is plainly exhibited.

Required the fifth power of 8 the root, or first first multiply by - - - 8 s = power.

then multiply the product 64 = 82 = square, or

by 8 [second power.

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What is the second power of 3.05? Ans. 9.3025

What is the third power of 85.3? Answer, 620650 477 .

What is the fourth power of .073 Answer, 090028398241

What is the eighth power of .09?. Answer, .00.00,00,0043046721

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