tor or quotient, it follows, that in division the decimal places of the dividend must be equal to the number of places in the divisor and quotient taken together. Hence, the number of decimal places in the quotient must equal the excess of those in the dividend above those in the divisor.

Divide 5-81224 by 5·432.

Dividing 581224 by 5432 we find 107 for the quotient. Since 5 figures of the dividend are decimals, and only 3 figures of the divisor are decimals, it follows that two figures of the quotient 107 must be decimals, so that 1.07 is the quotient sought.

Hence the following

RULE.

Divide as in whole numbers; give as many

decimal places

in the quotient as those in the dividend exceed those in the divisor; if there are not as many, supply the deficiency by prefixing ciphers.

How do you divide one decimal by another? How many decimal places must the quotient have? If the whole number of figures in the quotient is not as great as the number of decimals required, how do you proceed?

In this example, the dividend contains 6 decimal places, and the divisor but 1; therefore, by the rule, the quotient ought to contain 5; but as there are but 4 figures in the

quotient, we make up the deficiency by prefixing a cipher

55. When there are not as many decimal places in the dividend as in the divisor, we may, (by Art. 49,) annex as many ciphers to the dividend as we please, if we do not change the place of the decimal point. When the number of decimal places is the same in both dividend and divisor, the quotient will be a whole number. As for example, divided by =3, which is a whole number; that is, 0-6 divided by 0-2=3, a whole number.

When there are not as many decimal places in the dividend as in the divisor, how do you proceed? When the number of decimal places in the dividend is the same as in the divisor, what will the quotient be?

9. Divide 0.25 by 0·0005.

10. Divide 0.125 by 0·000005.

Ans. 36.

Ans. 10.

Ans. 500.

Ans. 25000.

56. When there is still a remainder, and we wish a more accurate quotient, we may continue to annex ciphers and to divide as far as we please, observing the rule for placing the decimal point.

When, in the quotient, we write the sign + it is to indicate that the quotient is still larger than is written.

It frequently happens, as in this example, that the work will never terminate.

When there is still a remainder, how may we proceed to obtain a still more accurate value for the quotient? What does the sign + at the right of a quotient indicate?

13. Divide 7.85 by 3.43. 14. Divide 0-478 by 0.58.

15. Divide 0·9009 by 0·4051.

Ans. 2-2886+.

Ans. 0.824+.

Ans. 2.223+.

57. We may, obviously, divide any decimal by 10, 100, 1000, &c., by removing the decimal point as many places to the left as there are ciphers in the divisor; when there are not so many figures at the left of the decimal point, we may prefix ciphers.

How may we divide a decimal by 10, 100, 1000, &c.? When in the decimal number there are not as many figures on the left of the decimal point as there are ciphers in the divisor, how do you proceed?

FEDERAL MONEY.

58. This is the currency of the United States. Its denominations, or names, are Eagles, Dollars, Dimes, Cents, and Mills.

Eagles,

Half Eagles,

are coined from gold.*

Quarter Eagles,

* See note at end of the subject of Federal Money.

59. The gold. for coinage is not pure, but consists of

of pure gold, of silver, and of copper; or, as usually expressed, 22 carats of gold, 1 of silver, and 1 of copper. A carat being part of the whole.

The standard for silver is 1489 of pure silver to 179 of pure copper; which, in carats, is 21 of silver, and 2o of copper.

The copper coins are of pure copper.

18, 1837, the %1% pure silver was to

By an Act of Congress, approved January gold and silver coin was to consist of metal, and alloy. The alloy for consist of pure copper, and the alloy for gold was to consist of copper and silver, provided that the silver does not exceed one half of the whole alloy.

The weight of the Eagle was fixed at 258 grains; the weight of the Dollar was to be 412 grains; that of the Cent was to be 168 grains.

* The symbol$ is probably a combination of the letters U. S., written $, to express United States money.