FEDERAL MONEY.

Federal Money is the coin of the United States; established by Congress, A. D. 1786. As the money of account proceeds in a decuple or ten-fold proportion, so any number of dollars, dimes, cents and mills, is simply the expression of dollars and decimal parts of a dollar Thus, 9 dollars and 8 dimes are expressed, 9,8 9, doll. 12 dollars, 4 dimes and 7 cents, thus: 12,47=12, doll. Hence, Federal Money is in all respects operated as decimals, and of all coins is the most simple and easy.

NOTE.

A dollar is the unit money; dollars, therefore, must stand the place of units, all less denominations being valued according to their place from the dollar's place. Dollars are separated from the inferiour denominations by a comma or seperatrix. Then the first figure at the right of this seperatrix is dimes, the second cents, and the third figure mills. All the figures at the left of the seperatrix are dollars; or you may call the first figure dollars, and all the figures to the left hand of dollars, or beyond the unit's place. are eagles; for as 10 dollars make one eagle, the dollars in the ten's place may be called units of eagles; the dollars in the hundred's place, tens of eagles, &c.

Thus, any sum of this money may be read differently, either wholly in the lowest denomination, or partly in the higher and partly in the lowest; as, for example, 46,75, may be either read 4675 cents, or 467 dimes and 5 cents, or 46 dollars, 7 dimes, and 5 cents, or 4 eagles, 6 dollars, 7 dimes and 5 cents.

A cypher at the right hand of the figures which are at the right of the seperatrix, does not alter the value; for 5,5 is five dollars and five dimes; and if you annex a cypher, thus, 5,50 it is still five dollars and five dimes, or five dollars and fifty cents, which is just the

same.

But if you prefix a cypher before the 5, thus, 5,05, it diminishes its valuean fold, by placing it in the cents' place; it being then five dollars and five cents.

NOTE.-In common reckoning no denominaations are mentioned but dollars and cents: 48,52, four eagles, eight dollars, five dimes and two cents, are read, forty-eight dollars and fifty-two cents. But accountants generally omit the comma, and distinguish cents from dollars by setting them apart from the dollars.

ADDITION OF FEDERAL MONEY.

RULE.

Place the numbers according to their value; that is, dollars under dollars, dimes under dimes, &c. and proceed exactly as in whole numbers.

EXAMPLES.

1. Add 32 eagles; 5 eagles, 6 dollars 8 cents; 17 dollars, 4 dimes 2 cents, 3 mills, 64 cents, 8 mills; 50 dollars, 7 cents, together.

OPERATION.

E. d. c. m.
32, 0

5, 6, 0 8

1, 7, 4, 2. 3
6 4, 8

5 0. 0, 7

$4 4, 4, 2, 2, 1

PROOF. Addition of Federal Money is proved exactly in the same way as addition of whole numbers: thus

8 excess in parts.
X

8 excess in sum.

SUBTRACTION OF FEDERAL MONEY.

RULE.

Place the numbers according to their values, and subtract as in whole numbers.

When the multiplier is an integer, multiply as in whole numbers, and the seperatrix will be as many figures from the right, in the product, as in the multiplicand.

20

Multiply as in whole number, and place the seperatrix in the product as many figures from the right as there are figures at the right of the seperatrix in both factors; as taught in multiplication of decimals. NOTE.-'I he figures in the fourth place at the right of the seperatrix, are tenths of mills, and in the fifth hundredths of mills, &c.

* As a dollar is to the unit, or integer, so the inferiour denominations, being less than a dollar, are fractions of unity, or less than an integer. If integers be multiplied by integers, the product will be integers; but if integers be multiplied by less than integers, the product will be as much less than integers as the multiplier is less than integers. Thus dollars multiplied by dollars produce dollars; dollars multiplied by dimes produce dimes; dimes multiplied by dimes are tenths of dimes; dimes by cents produce tenths of cents, and cents by cents produce hundredths of cents; mills by mills produce thousandths of mills, &c.

DIVISION OF FEDERAL MONEY.

CASE 1. When the divisor is an integer.

RULE. Divide as in whole uumbers; observing to make the seperatrix in the quotient, when you have divided all the integers in the dividend.

NOTE. The remainder, if any, may be brought into lower denominations, by annexing cyphers, and then it may be divided again.

CASE 2. When the divisor is a number of more than one denomination.

RULE.

Divide as before, but make not the seperatrix in the quotient till you have divided as many figures past the seperatrix in the dividend as there are figures at the right of seperatrix, in the divisor. If there be not as many figures at the right of the seperatrix, in the dividend, as in the divisor, the defect may be supplied by annexing cyphers.

NOTE. You may make the figures, at the right of the seperatrix, in the dividend and divisor, equal by annexing cyphers.