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phers to the remainder, to continue the division as far as necessary.

4. The first figure of the quotient will possess the same place of integers or decimals, as that figure of the dividend which stands over the unit's place of the first product.

EXAMPLES. 1. Divide 3424,6056 by 43,6. Divisor. Dividend. Quotient. 43,6)3424,6056(78,546 3052

Or, What is potash per

ton, when 43 tons, 12cwt. 3726

cost $3424,6056? 3488

Ans. $78,54c. 6m.

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13. If 21% or 21,75 yards of cloth cost 34,517dols., what is the price of one yard ? Ans. 1,586 dol. t

Note -When decimals or whole numbers, are to be divided by 10, 100, 1000, &c. (viz. unity with ciphers,) it is performed by removing the separatrix in the dividend, so many places towards the left hand, as there are ciphers in the divisor.

EXAMPLES

( 10 the quotient is 74,8dols. $748 divided by 100 : - 7,48dols.

(1000 - - ,748dol.

REDUCTION OF DECIMALS.

CASE I.
To reduce a Vulgar Fraction to its equivalent decimal.

Rule.-Divide the numerator by the denominator, an-nexing as many ciphers as are necessary; and the quotient will be the decimal required.

EXAMPLES 1. Reduce to a decimal.

*24)5,0000(,20833+ Ans.

48

200
192

30

8 Remainder. 2. Required the equivalent decimal expressions for 4, 1 and

Ads. ,25 ,5 and ,75. 3. Reduce to a decimal.

Ans. ,375. · 4. Reduce and to decimals. Ans. ,04 and ,407,+

5. Reduce and his to decimals.

Ans.,88 and ,00689.+

CASE II. To reduce numbers of different denominations to their

equivalent decimal values. RULE I.—Write the given numbers perpendicularly under each other for dividends, proceeding orderly from the least to the greatest.

2. Opposite to each dividend, on the left hand, place such a number for a divisor, as will bring it to the next superiour denomination, and draw a line between them.

3. Begin with the uppermost, and write the quotient of each division, as decimal parts, on the right hand of the dividend next below it; and so on until they are all used, and the last quotient will be the decimal sought.

EXAMPLES. 1. Reduce 15s. 9 d. to the decimal of a pound.

4] 3,

12 9,75
- 2015,8125

,790625 the decimal required. 2. Reduce 19s. to the decimal of a pound.

Ans. ,95. 3. Reduce 10s. 9d. lqr. to the decimal of a pound.

Ans. ,5385416. + 4. Reduce 1d. 2qrs. to the decimal of a shilling

Ans. ,125. 5. Reduce 10oz. 18dwt. 16grs. to the decimal of a tt

Ans. ,911111.t 6. Reduce 10oz. 14drs. to the decimal of a hundred weight.

Ans. ,0060686.+ 7. Reduce 3 rods 24feet, 6 inches to the decimal of a mile.

Ans. ,00994318. + .8. Reduce 1 pint to the decimal of a gallon.

Ans. ,125. 9. Reduce 2 months, 2 weeks, 2 days to the decimal of a year,

Ans. ,197802.+

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10. Reduce 3s. 4d. New-England currency to the decimal of a dollar.

Ans. ,555555.+

CASE III. To reduce any number of shillings, pence and farthings

by inspection to the decimal of a pound. Rule.-Write half the greatest even number of shillings for the first decimal figure, and let the farthings in the given pence and farthings possess the second and third places; observing to increase the second place by 5, if the shillings be odd; and the third place by one, when the farthings exceed 12, and by 2, when they exceed 36.

EX.4 MPLES.
1. Find the decimal of 15s. 8 d. by inspection.

,7= of 14s.
,05 for the odd shilling.
,034=farthings in 8 d.
,001 for excess above 12.

,785=decimal required. 2. Find by inspection the decimal of 12s. 6 d.

Ans. ,628. 3. Find by inspection the decimal of 188. 104d.

i Ans. ,943. 4. Find by inspection, and add together the decimal of 13s. 6d., 9s., 1s. 93., 5d., and 1d. Ans. £1,242.+

Case IV. To find the value of any given decimal in terms of the

integer. RULE 1.--Multiply the decimal by the number of parts in the next less denomination, and cut off as many places for a remainder on the right hand, as there are places in the given decimal. . . .

2. Multiply the remainder by the parts in the next inferior denomination, and cut off for a remainder as before.

3. Proceed in this manner through all the parts of the integer, and the several denominations, standing on the left hand, will make the answer.

EXAMPLES 1. What is the value of ,7426 of a pound ?

;7426

20

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Case V. To find the value of any decimal of a pound by inspection.

Rule.--Double the first figure or place of 10ths for shillings, and if the second be five, or more than 5, add another shilling, then call the figures in the second and third places, after the 5 (if contained) is deducted, farthings; abating 1 if their number is more than 12, and two if more than 36 ; the result will be the answer.

EXAMPLES.
1. Find the value of ,785£ by inspection.

14s.=double 7.
Is. for 5 in the place of 10this.

83=35 karthings.
.. abated for the excess above 12.

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