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9. Reduce 54 gallons to the fraction of a hogshead of wine.

Ans.

Ans. & fo. What part of a hogshead is 9 gallons? 11. What part of a pound troy is 10oz. 10pwt. 10grs.?

DECIMAL FRACTIONS.

Ans. 19

A Decimal Fraction is that whose denominator is an unit, with a cypher, or cyphers annexed to it, Thus, I, Too? TOO, &c. &c.

45

The integer is always divided either into 10, 100, 1000, &c. equal parts; consequently the denominator of the fraction will always, be either 10, 100, 1000, or 10000, &c. which being understood, need not be expressed; for the true value of the fraction may be expressed by writing the numerator only with a point before it on the left hand thus, is written,5; 6,45; 73,725, &c.

But if the numerator has not so many places as the denominator has cyphers, put so many cyphers before it, viz. at the left hand, as will make up the defect; so write thus, ,05; and thus, ,006, &c.

NOTE. The point prefixed is called the separatrix. Decimals are counted from the left towards the right hand, and each figure takes its value by its distance from the unit's place; if it be in the first place after units, (or separating point) it signifies tenths; if in the second, hundredths, &c. decreasing in each place in a tenfold proportion, as in the following NUMERATION TABLE.

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Cyphers placed at the right hand of a decimal fraction do not alter its value, since every significant figure contianes to possess the same place: so,5,50 and ,500 are adresa ne value, and equal to or

5

10

Ferners placed at the left hand of decimals, decrease teir value in a tenfold proportion, by removing them further from the decimal point. Thus,,5 ,05,005, &c. are five tenth parts, five hundredth parts, five thousandt parts, &c. respectively. It is therefore evident that the magnitude of a decimal fraction, compared with another, does not depend upon the number of its figures, but upon the value of its first left hand figure: for instanee, a fraction beginning with any figure less than 9 such as ,899209, &c. if extended to an infinite number of figures, will not equal ,9.

ADDITION OF DECIMALS.

RULE.

1. Place the numbers, whether mixed or pure decimal under each other, according to the value of their places 2. Find their sum as in whole numbers, and point ch so many places for the decimals, as are equal to the greatest number of decimal parts in any of the given numbers.

EXAMPLES.

1. Find the sum of 41,653-1-36,05+24,009+1,6.

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Sum, 103,312 which is 103 integers, and 12 parts of an unit. Or, it is 103 units, and 3 tenth parts, 1 hundredth part, and 2 thousandth parts of an unit, or 1.

Hence we may observe, that Decimals, and FEDERAL MONEY, are subject to one, and the same law of notation And consequently of operation.

For since dollar is the money unit; and a dime being the tenth, a cent the hundredth, and a mill the thousandth part of a dollar, or unit, it is evident that any number of dollars, dimes, cents and mills, is simply the expression of dollars, and decimal parts of a dollar: Thus, 11 dollars, 6 dimes, 5 cents, 11,65 or 11,65 dol. &c.

2. Add the following mixed numbers together.

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(4) Dollars.

48,9103

1,8191

3,1030

,7012

5. Add the following sums of Dollars together, viz. $12,54565+7,891+2,54+14,+,0011

Ans. 856,57775, or $56, 5di. 7cts. 7-75mills. 6. Add the following parts of an acre together, viz, ,7569+,25+,654+,199

Ans. 1,8599 acres.

7. Add 72,5--32,071+2,1574+371,4+2,75

8. Add 50,07-200,71+59,4+5207,1

Ans. 480,8784

Ans. $497,28

9. Add 71,467+27,94+16,084+-98,009+86,5

10. Add ,7509+,0074+,69+,8408+,6109

11. Add ,6+,099+,37+,905+,026

Ans. 500

Ans. 2,9

Ans. 2

12. To 9,999999 add one millionth part of an unit

and the sum will be 10.

13. Find the sum of

Twenty-five hundredths,

Three hundred and sixty-five thousandths,

Six tenths, and nine millionths,

Answer, 1,215009

SUBTRACTION OF DECIMALS.

RULE.

Place the numbers according to their value; then subtract as in whole numbers, and point off the decimals as in Addition.

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13. From an unit, or 1, subtract the millionth part of

itself.

ins. ,999999

MULTIPLICATION OF DECIMALS.

RULE.

1. Whether they be mixed numbers, or pure decimals, place the factors and multiply them as in whole numbers. 2. Point off so many figures from the product as there are decimal places in both the factors; and if there be not so many places in the product, supply the defect by prefixing cyphers to the left hand.

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7. Multiply

,004 by ,004

,000016

8. What cost 6,21 yards of cloth, at 2 dols. 32 cents, 5 mills, per yard ? Ans. $14, 4d. 3c. 88m. 9. Multiply 7,02 dollars, by 5,27 dollars.

Ans. 36,9954dols. or $36 99cts. 5m. 10. Multiply 41 dols. 25 cts. by 120 dollars." Ans. $4950

11. Multiply 3 dols. 45 cts. by 16 cts.

Ans. 80,552055cts. 2mills.

12. Multiply 65 cents, by ,09 or 9 cents.

Ans. $0,0585=5cts. 81mills.
Ans. $1

13. Multiply 10 dols. by 10 cts.
14. Multiply 341,45 dols. by ,007 or 7 mills.
Ans. $2,39+

To multiply by 10, 100, 1000, &c. remove the separating point so many places to the right hand, as the multiplier has cyphers.

So ,425

Multiplied by 10,

by 100,

makes 4,25
makes 42,5

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425,

For ,425×10 is 4,250, &c.

DIVISION OF DECIMALS.

RULE.

1. The places of the decimal parts of the divisor and ayotient counted together, must always be equal to those

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