§ 3. Federal Money.

FEDERAL MONEY is the coin of the United States, established by Congress, A. D. 1786. Of all coins this is the most simple, and the operations in it, the most easy.

THE denominations are in a decimal proportion, as exhibited in the following

THE expression of any sum in Federal Money is simply the expression of a mixed number in decimal fractions. A dollar is the Unit money; dollars therefore must occupy the place of units, the less denominations, as dimes, cents, and mills, are decimal parts of a dollar, and may be distinguished from dollars in the same way as any other decimals by a comma or separatrix. All the figures to the left hand of dollars, or beyond units place are eagles. Thus, 17 Eagles, 5 dollars, 3 dimes, 4 cents, and 6 mills are written

Or these, four are real coins, and one is imagin

ary.

THE real coins are the Eagle, a gold coin; the Dollar and the Dime, silver coins; and the Cent, a copper coin. The mill is only imaginary, there being no piece of money of that denomination.

THERE are half-eagles, half-dollars, double-dimes, half-dimes, and half-cents, real coins.

THESE denominations, or different pieces of money, being in a tenfold proportion, consequently, any sum in Federal Money does of itself exhibit the particular number of each different piece of money contained in it. Thus, 175,346 (seventeen eagles, five dollars, three dimes, four cents, six mills) contain 175346 mills, 17534 cents, 1753 46 dimes, 175-346 dollars, 176346 eagles. Therefore, eagles and dollars reckoned together, express the number of dollars contained in the sum, the same of dimes and cents; and this indeed is the usual way of account, to reckon the whole sum in dollars, cents, and mills thus,

100

1000

10000

THE Addition, Subtraction, Multiplication and Division of Federal Money is performed in all respects as in Decimal Fractions, to which the Scholar is referred for the use of rules in these operations.

ADDITION of FEDERAL MONEY.

1. ADD 16 Eagles; 3 Eagles, 7 Dollars, 5 Cents; 26 Dollars, 6 Dimes, 4 Cents, 3 Mills; 75 Cents, 8 Mills; 40 Dollars, 9 Cents together.

2. IF I am indebted 59 dollars, 212 dollars, 98 cts, 113 dolls. 15 cts. 15 dolls. 21 dolls. 50 cts. 200 dolls. 73 dolls. 35 dolls. 17 cts. 75 dolls. 20 dolls. 40 dolls. 33 cts. and 16 dolls. What is the sum which I owe?

Ans. 781 13

ACCOUNTANTS generally omit the comma and distinguish cents from dollars by setting them apart from the dollars.

SUBTRACTION of FEDERAL MONEY.

1. FROM Dolls. 863,17

take, Dolls. 69,82

OPERATION

8 63, 17
69,8 2

Remainder, 7 9 3, 3 5

2. FROM Dolls. 681 take, Dolls. 57,63 Remainder, Dolls. 623,37

MULTIPLICATION of FEDERAL MONEY,

1. IF Flour be Dolls. 10,25 per barrel what will 27 barrels cost?

DIVISION of FEDERAL MONEY.

1. IF 2728 bushels of wheat cost Dolls. 2961, how much is it per bushel ?

2. DIVIDE Dolls. 3756 equally among 13 men; what will each man receive ? Ans. Dolls. 288,923

3. DIVIDE Dolls. 16,75 by 27. Product, 62 cents!

REDUCTION of FEDERAL MONEY.
CASE 1.

To reduce Pounds, Shillings, Pence and Farthings, to Dollars,
Cents and Mills.
RULE.

SET down the pounds and to the right hand write half the greatest even number of the given shillings; then consider how many farthings there are contained in the given pence and farthings, and if the sum exceed 12, increase it by 1, or if it exceed 36, increase it by 2, which sum set down to the right hand of half the greatest even number of shillings before written, remembering to increase the second place, or the place next to shillings by 5, if the shillings be an odd number; to the whole sum thus produced, annex a cypher and divide the sum by 3; cut off the three right hand figures in the quotient, which will be cents and mills, the rest will be dollars.

EXAMPLES.

F. REDUCE 47 7s. 103d. to Dollars, Cents, and Mills.

In this example to the right hand of pounds (47) I write 3, half the greatest even number of the given shillings (7,) the farthings in 10 d.(43) increased by two(45) because exceeding 36 and the second place increased by 5 because the shillings were an odd number, are 95, which sum written to the right hand of the 3,a cypher annexed,and the sum divided by 3, gives the Answer, 157 dollars, 98 cents, and 3 mills.

DIVIDE by 3) 4 7 3 9 5 Q

Dolls. 1 5 7,9 8 3

3.

Ir pounds only are given to be reduced, a cypher must be annexed and the number divided by 3: the quotient will be dollars. If there be a remainder annex more cyphers, and divide, the quotient will be cents and mills.

WHEN there are no shillings, or only 1 shilling in the given sum, so there be ne even number, write a cypher in place of half the even number of shillings, then proceed with the pence and farthings as in other cases.

Ir it be required to reduce pounds, shillings, pence, &c. to Dollars and cents only, the cypher must not be annexed; in this case two figures only must be out off from the quotient.

A LITTLE practice will make these operations extremely easy:

To reduce Dollars, Cents, and Mills, to Pounds, Shillings, Pence, and Farthings. RULE.

MULTIPLY the given sum by 3, cut off the four right hand figures; which will be decimals of a pound, the left hand figures will be the pounds. To find the value of the decimals, double the first figure for shillings, and if the figure e second place be 5, add another shilling, then call the figures in the secand third places, after deducting the 5 in the second place, so many farugs, abating 1 when they are above 12, and 2, when they are above 36.