« ΠροηγούμενηΣυνέχεια »
Note.—Many foreign coins are still in circulation. Indeed some of the rates of postage established by the government, were, until recently, adapted to foreign coins. To the last Congress belongs the honor of abolishing these anti-national rates, and of establishing others in Federal Money.
203. The national coins of the United States are of three kinds, viz: gold, silver, and copper.
1. The gold coins are the eagle, half eagle, and quarter eagle.
The eagle contains 270 grains of standard gold; the half eagle and quarter eagle like proportions.
2. The silver coins are the dollar, half dollar, quarter dollar, the dime, and half dime.
The dollar contains 416 grains of standard silver; the others, like proportions.
3. The copper coins are the cent and half cent.
The cent contains 264 grains of pure copper, or 100 cents contain 24 pounds avoirdupois ; the half cent, a like proportion
Mills are not coined.
Obs. 1. The fineness of gold used for coin, jewelry, and other purposes, also the gold of commerce, is estimated by the number of parts of gold which it contains. Pure gold is supposed to be divided into 24 equal parts, called carats. Hence, if it contains 10 parts of alloy, or some baser metal, it is said to be 14 carats fine ; if 5 parts of alloy, 20 carats fine; and when absolutely pure, it is 24 carats fine.*
2. The standard for gold coins in the United States is of puro gold, of silver, and 24 of copper, and is therefore said to be 22 carats fine.
3. The standard for silver coins is 1489 parts of pure silver to 179 parts of pure copper.
204. All accounts are kept in dollars, cents, and mills.
Quest.–203. Of how many kinds are the coins of the United States ? What are they? What are the gold coins? The silver coins? The copper? Obs. How is the fineness of gold estimated ? Into how many carats is pure gold supposed to be divided ? When it contains 10 parts of alloy, how fine is it said to be? 5 parts of alloy? 2 parts? 4 parts ? How many carats fine are the gold coins of the United States ? What are the other two parts? What is the standard for silver coins ? 204. In what are accounts kept? How would you express 5 eagles ? 7 E. and 5 dolls.? 10 E.! How express 6 dimes? 8 dimes? 10 dimes ?
* Silliman's Chemistry.
Eagles are expressed in dollars, and dimes in cents.Thus, instead of 5 eagles, we say, 50 dollars; instead of 7 eagles and 5 dollars, we say, 75 dollars, &c. So, instead of 6 dimes, we say, 60 cents ; instead of 8 dimes and 7 cents, we say, 87 cents, &c.
205. It will be seen from the table, that the denominations of Federal Money increase and decrease in value from right to left and left to right, in a tenfuld ratio ; and that it is expressed, like simple numbers, by the Decimal or Arabic Notation.
206. The Dollar is regarded as the unit ; cents and mills are fractional parts of the dollar, and are distinguished from it by a decimal point or separatrix (.) in the same manner as common decimals. (Art. 179.) Dullars therefore occupy units' place of simple numbers; eagles or tens of dollars, tens' place, &c. Dimes, or tenths of a dollar, occupy the place of tenths in decimals ; cents, or hundredths of a dollar, the place of hundredths ; mills, or thousandths of a dollar, the place of thousandths ; tenths of a mill, or ten thousandths of a dollar, the place of ten thousandths, &c.
Obs. 1. Since dimes business transactions are expressed in cents, two places of decimals are assigned to cents. If therefore the number of cents is less than 10, a cipher must always be placed on the left hand of them ; for cents are hundredths of a dollar, and hundredths occupy the second decimal place. (Art. 181.) For example, 4 cents are written thus .04; 7 cents thus .07; 9 cents thus .09, &c.
2. Mills occupy the third place of decimals; for they are thousandths of a dollar. Hence, when there are no cents in the given sum, two ciphers must be placed before the mills.
207. Hence, to read any sum of Federal Money.
Call all the figures on the left of the decimal point dollars; the first two figures after the point, are cents; the
205. How do the denominations of Federal Money increase and decrease? How is it expressed ? 206. What is regarded as the unit in Federal Money? What are cents and mills ? How are they diytinguished from dollars ? 207. How do you read Federal Money? Oos. What other mode of reading Federal Money is mentioned?
third figure denotes mills; the other places on the right are decimals of a mill. Thus, $3.25232 is read, 3 dollars, 25 cents, 2 mills, and 32 hundredths of a mill.
Obs. Sometimes all the figures after the point are read as decimals of a dollar. Thus, $5.356 is read, “5 and 356 thousandths dollars."
Read the following sums of Federal Money:
Write the following sums in Federal Money : 4. 63 dollars and 85 cents.
Ans. $63.85. 5. 150 dollars and 73 cents. 6. 201 dollars and 9 cents. 7. 300 dollars, 5 cents, and 3 mills. 8. 4 dollars, 6 cents, and 8 mills. 9. 100 dollars, 7 cents, 5 mills, and 3 tenths of a mill. 10. 1000 dollars, 6 mills, and 36 hundredths of a mill.
Note.--In business transactions, when dollars and cents are expressed together, the cents are frequently written in the form of a common fraction. Thus, $76.45 are written 7610 dollars.
REDUCTION OF FEDERAL MONEY.
Ex. 1. How many cents are there in 75 dollars ?
Suggestion. Since in 1 dollar there are 100 cents, in 75 dollars there are 75 times as many. And 75 X 100= 7500.
Ans. 7500 cents.
2. In 9 cents, how many mills ? Ans. 90 mills. 3. In 25 dollars, how many mills ? Ans. 25000 mills.
Note-To multiply by 10, 100, &c., is simply annexing as many ciphers to the multiplicand, as there are ciphers in the multiplier. (Art. 59.) Hence,
208. To reduce dollars to cents, annex two ciphers. To reduce dollars to mills, annex three ciphers. To reduce cents to mills, annex one cipher.
OBs. To reduce dollars and cents to cents, erase the sign of dollars and the separatriz. Thus, $25.36 reduced to cents, becomes 2536
4. In $5, how many cents ?
10. In 4500 cents, how many dollars ?
Suggestion. Since 100 cents make 1 dollar, 4500 cents will make as many dollars as 100 is contained times in 4500. And 4500-100=45.
11. In 150 mills, how many
cents ? Ans. 15 cents. 12. In 25000 mills, how many
dollars ? Ans. $25. Note.-To divide by 10, 100, &c., is simply cutting off as many figures from the right of the dividend as there are ciphers in the divisor. (Art. 80.) Hence,
209. To reduce cents to dollars, cut off two figures on the right.
To reduce mills to dollars, cut off three figures on the right.
To reduce mills to cents, cut off one figure on the right. Obs. The figures cut off are cents and mills.
QUEST.-208. How are dollars reduced to cents? Dollars to mills ? Cents to mills? Obs. ;)ollars and cents to cents? 209. How are cents reduced to dollars ? Mills to dollars? Mills to cents ? Obs. What are the figures cut off ?
13. In 325 cents, how many dollars ? Ans. $3.25. 14. In 423 mills, how many cents ? Ans. 42c. 3m. 15. In 4320 mills, how many dollars ? 16. How many dollars in 63500 cents ? 17. How many cents in 4890 mills ?
210. Since Federal Money is expressed according to the decimal system of notation, it is evident that it may be subjected to the same operations and treated in the same manner as decimal fractions.
ADDITION OF FEDERAL MONEY.
Ex: 1. A man bought a cow for $15.75, a calf for $2.375, a sheep for $3.875, and a load of hay for $8.68: how much did he pay for all ? Operation. We write the dollars under dollars, cents 15.75 under cents, &c. Then add each column 2.375 separately, and point off as many figures 3.875 for cents and mills, in the amount, as there
8.68 are places of cents and mills in either of $30.680 Ans.
the given numbers.
211. Hence, we derive the following
Write dollars under dollars, cents under cents, fc., so that the same orders or denominations may stand under each other. Add each column separately, and point off the amount as in addition of decimal fractions. (Art. 187.)
Obs. If either of the given numbers have no cents expressed, it is customary to supply their place by ciphers.
2. A farmer sold a firkin of butter for $9.28, a cheese for $1.17, a quarter of veal for 56 cents, and bushel of wheat for $1.12 : how much did he receive for the whole ?
Quest.-211. How is Federal Money added? How point off the amount? Obs. When any of the given numbers have no cents expressed, how is their place supplied ?