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 cipher 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. 900 By an Act of Congress, approved January 18, 1837, the gold and silver coin was to consist of 1% pure metal, and alloy. The alloy for silver was to 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. Where is Federal Money used? What are its denominations? Which are coined from gold? Which from silver? Which from copper? Which one is never coined? What metals are mixed with gold for coining? In gold coins, what is the ratio of the copper and silver to the gold? What is a carat? What is the standard for silver coins? What is the ratio when estimated in carats? Is the copper for copper coins also alloyed? By Act of Congress, 1837, what fractional part of gold and silver coin is pure metal? And what part is alloy? Of what metal is the alloy for silver? Of what metals is the alloy for gold? What is the weight of the Eagle? What is the weight of the Dollar? What the weight of the Cent? Repeat the table of Federal Money. 60. Since the different denominations succeed each other in a ten-fold ratio, as in whole numbers and decimals, it is plain that the preceding rules for decimals are applicable to this currency. The United States was the first, and only government, that adopted the decimal division for its currency. It is much to be regretted that they did not, at the same time, give the decimal division to their weights and measures. Notwithstanding the great simplicity of the decimal division, a large number of our merchants mark their goods in shillings and pence, and some even keep their book accounts in English currency. The rates of postage, having been fixed in Federal currency, will do much towards bringing about its universal use in the United States. Federal money ought never to be treated as consisting of different denominations, since it is by far the simplest and best way to consider its denominations the same as decimals. To make this more clear, we will give the following table of Federal Money: &c. &c. TABLE. 4 Thousands of dollars. Hundreds of dollars. → → → Tens of dollars, or eagles. Units or ones, or dollars. Tenths of a dollar, or dimes. 4 4 4 4 4 4 4 4 4 84444, 44 cents, 4 mills. 4 4 4 4 4 4 $444, 44 cents, 4 mills. It is customary, in accounts, to use only dollars, cents, and mills, so that eagles are expressed in dollars, and dimes in cents. In what ratio do the different denominations of Federal Money decrease? Are the rules for decimals applicable to this currency? Should Federal Money be treated as denominate numbers? In accounts, which denominations only are used? How, then, are Eagles expressed? How are Dimes expressed? Thus 5 eagles and 6 dollars is the same as 56 dollars. 4 dimes and 5 cents is the same as 45 cents. 3 dimes 3 cents and 3 mills is the same as 333 mills. 2 dimes and 2 mills is the same as 202 mills. 1 dollar is the same as 100 cents, which is 1000 mills. 2 dollars is the same as 200 cents, which is 2000 mills. 5 dollars is the same as 500 cents, which is 5000 mills. 7 dollars is the same as 700 cents, which is 7000 mills. 56 dollars is the same as 5600 cents, which is 56000 mills. 365 dollars is the same as 36500 cents, which is 365000 mills. 3456 dollars is the same as 345600 cents, which is 3456000 mills. &c. &c. From this we see that dollars are changed into cents by annexing two ciphers; cents are changed into mills by annexing one cipher, and dollars into mills by annexing three ciphers. How are dollars changed into cents? How are cents changed into mills? How are dollars changed into mills? EXAMPLES. 1. How many cents in $6? 2. How many mills in 13 cents? 3. How many mills in $4 and 45 cents? Ans. 600. Ans. 130. Ans. 4450. 4. How many mills in 75 cents and 1 mill? Ans. 751. 5. How many cents in $9 and 13 cents? Ans. 913. 6. How many mills in $5 and 55 cents and 5 mills? Ans. 5555. 61. If we cut off one figure from the right of mills, which is dividing by 10, (ART. 30,) the sum will be changed into cents; if from the right of cents we cut off two figures, that is, divide by 100, the sum will be changed into dollars; and if from the right of mills we cut off three |