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Reduction of Decimals.

CASE I. To reduce a vulgar fraction to its equivalent decimal fraction.

RULE.

Divide the numerator by the denominator, as in division of decimals, annexing cyphers to the right hand of the numerator as far as neceffary : So shall the quotient be the equivalent decimal fraction required.

EXAMPLE Reduce d, and t, and i to decimal fractions. 4)1.001.25 Ans.

2)1.0.5 Ans.

4)3.001.75 Ana 8

28

IO

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Ex.

275
Reduce
5.

to a decimal frac. Ans..071577&c.* 3842

Ex. 6. Reduce I to a decimal frac. Ans. .291666 &c.*

24

CASE II. To find the value of a decimal fraction in terms of the inferior denomination.

RULE. Multiply the decimal fraction by the number or parts in the next lower denominator ; and point off as many places for a remainder, to the right hand, as there are places in the given decimal fraction.

Multiply that remainder by the number of parts in the next lower denomination again, pointing off for another remainder as before.

Proceed in the fame manner through all the parts of the integer ; then the several denominations separated on the left hand, will make up the answer.

EXAMPLE
What is the value of .775 of a pound currency?

:775
Multiply by 20 shillings in a pound.

(15.500
Multiply by 12 pence in a shilling.
d6.000

Ans. /15 6d.

* The answers of the 5th & 6th examples are circulating repetends.

Ex. 2. What is the value of.875 gallon ? Ans. 7 pints. Ex.3, What is the value of .75 foot ? Ans. 9 inches. Ex. 4. What is the value of .623.?

Ans. 7 d. Ex. 5. What is the value of .0125lb Troy? Ans. 3dwts. Ex. . What is the value of .46941b Troy?

Ans. 5oz. 12dwts. 15:744gr. Ex. 7. What is the value of .625cwt? Ans. 2qr. 141b. Ex. 8. What is the value of .328125 ton ?

Ans. 6cwt. 2qr. 71b. Ex. 9. What is the value of .25 cubick foot ?

Ans. 432 cubick inches.

CASE III. To reduce integers or decimals to equivalent decimals of higher denominations.

RULE. Divide by the number of parts in the next higher denomination; continuing the operation to as many higher denominations as may be necefsary, the same as in reduction ascending of whole numbers.

EXAMPLE. Reduce idwt. to the decimal fraction of a pound Troy.

Or thus, 240)1.000.004166 &c. Ans. ilb. 12oz.

960 201dwt.

IOZ. 2odwt.
I2|0.0502.
Ip.0041661b. Ans. 240dwts.

240

400

1600
1440

1600
1440

160 IX. 2. Reduce gd, to the decimal of a pound. Ans. £.0375 Ex. 3. Reduce 9 inches to the decimal of a foot.

Ans. 75 foot. Ex. 4. Reduce 2.15lb to the decimal of a cwt.

Ans..019196cwt.

Ex. 5. Reduce 1.5 pint to the decimal of a gallon.

Ans. .1875 gal. Ex. 6. Reduce .21 pint to the decimal of a peck.

Ans. .013125 peck.

CASE IV. To reduce the known parts of money, weight, measure, &c. to a decimal fraction.

RULE.

Write the given numbers directly under one another, the least being uppermost, and on their left draw line : Let these be reckoned as dividends.

Against each number or name on the left hand, write the number making one of its next superior name : And let these be divisors to the former dividends.

Begin with the upper one, and write the quotient of each division as fractions, on the right of the division next below it ; then let this mixed number be divided by its divisor, &c. And the last quotient will be the decimal fraction fought. Or

To the number of parts of the lesser denomination given, annex a competent number of cyphers, and divide by the number of such parts that are contained in the greater denomination, to which the decimal is to be brought, and the quotient is the decimal fraction fought.

EXAMPLE.

I

Reduce 1%. 2 d. to the decimal fraction of a pound. 411 Or I . 24 d.=57. 960)57.004.0593751. I 2 2.25

48.00 20 1.1875 2012 =96oqrs. 10.059375

9000
8640

Ans. 18.2 &d=.0593751.

3600
2880

7200
6720

4800
4800

I lb.

or

20 12

Ex. 2. Reduce 8oz. 15dwt. 18gr. to the decimal of a pound Troy. S4118 Or 8 oz. 15 dwt. 18 gr. 4218

1b. Troy. 24{*(4-5

=.7322916 &c. 15.75

12 OZ. 5760
8.7875
0.7322916 &c.

Ans. 8oz. 15dwt. 18gr.=.7322916 &c. lb. Troy. Ex. 3. Reduce 3qrs. 191b. 1402. to the decimal of a hun. dred weight.

Ans. .927455cwt. Ex.4. Reduce gcwt. Iqr. 16lb. to the decimal of a ton.

Ans. .469642+ton. Decimal Tables. Decimal tables are useful in redůcing inches to the de cimal of a foot, pints to the decimal of a gallon, pecks to the decimal of a bushel, &c. Also for finding the value of decimals.

! Deci Decimals of mals of a gallon. a Foot.

Inches.

Ounces.
Decimals of
a pound or
oz. Avord.
Drams.

Pints.

Qr. cwt.
Decimals of
a cwt. or
bushel.
Pecks.

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