fore if 3 be divided by 4, the quotient is the answer required.

Reduce to a decimal fraction. Answer .4

Reduce,,,, and so on to 3, to their corresponding decimal fractions; and in this operation the various modes of interminate decimals. may be easily observed.

RULE II.

To reduce Quantities of the same, or of different denominations to Decimal Fractions of higher denominations.

If the given quantity consist of one denomination only, write it as the numerator of a vulgar fraction; then consider how many of this make one of the higher denomination, mentioned in the question, and write this latter number under the former, as the denominator of a vulgar fraction. When this has been done, divide the numerator by the denominator, as directed in the foregoing rule, and the quotient resulting will be the decimal fraction required.

But if the given quantity contain several denominations, reduce them to the lowest term for the numerator; reduce likewise that quantity, whose fraction is sought, to the same denomination for the denominator of a vulgar fraction; then divide as before directed.

EXAMPLES.

Reduce 9 inches to the Decimal of a foot.

The foot being equal to 12 inches, the vulgar fraction will be ; then 12)9.00

.75 decimal frac

[tion required.

Reduce 8 inches to the decimal of a yard.

8 inches.

1 yard × 3 × 12= 36 inches.

36)8.0(.22+ = Answer.

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

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 lower 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.

The value, therefore, is 1 rood 14 perches.

What is the value of .6875 of a yard?

What is the value of .084 of a furlong?

per. 1 yd. 2 ft. 11 in.

Ans. 3

What is the value of .683 of a degree? Ans. 40

m. 58 sec. 48 thirds.

What is the value of .0053 of a mile?

per. 3 yds. 2 ft 5 in.+

Ans. 1

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?

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

If 187 dollars 85 cents gain 12 dollars 33 cents interest in a year, at what rate per cent is this interest? Ans. 6.56+

SECTION II.

INVOLUTION AND EVOLUTION.

INVOLUTION is the method of raising any number, considered as the root, to any required power.