FEDERAL MONEY. 203. Federal Money, we have seen, is the currency of the United States. Its denominations are Eagles, dollars, dimes, cents, and mills. (Art. 146.) Note. For the Table of Federal Money, the weight, and purity of its different coins, see Art. 146. 204. Federal Money is based upon the Decimal Notation; its denominations increase and decrease from right to left and left to right in a tenfold ratio, like simple numbers. It is therefore one of the most convenient and comprehensive systems of currency ever invented. 205. The dollar is regarded as the unit; cents and mills are fractional parts of the dollar, and are separated from it by a decimal point or separatrix (.), as decimals are separated from whole numbers. (Art. 179.) Thus, Dollars occupy units' place of simple numbers; eagles, or tens of dollars, tens' place; dimes, or tenths of a dollar, the place of tenths; 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. 206. Accounts, in the United States, are kept in dollars, cents, and mills. Eagles are expressed in dollars, and dimes in cents. Thus, instead of five eagles, we say 50 dollars; instead of 6 dimes, we say, 60 cents, &c. OBS. 1. Since dimes in 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 example, 4 cents are written thus .04; 7 cents thus .07; 9 cents thus .09, &c. 2. Mills occupy the third place of decimals; therefore, when there are no cents in the given sum, two ciphers must be placed before the mills. Hence, QUEST. 203.-What is Federal Money? What are its denominations? Re cite the Table. 204. Upon what is Federal Money based? 205. What is re garded as the unit in Federal Money? What are cents and mills considered? How are they distinguished from dollars? 206. How are accounts kept in the United States? How are Eagles expressed? Dimes? Obs. How many places are assigned to cents? When the number of cents is less than ten, what must be done? Wher no cents are mentioned, what do you do? 207. To read Federal Money. Call all the figures on the left of the decimal point, dollars; the first two figures on the righ of the point, conts; the third figure, mills; the other places on the right, decimals of a mill. Thus, $3.25232 is read, 3 dollars, 25 cents, 2 mills, and 32 hundredths of a inill. OBS. Sometimes all the figures afte the point are read as decimals of a dol ar. Thus, $5.356 is read, "5 and 35 thousandths dollars." Read the following sums of Federal Money. 1. $250.56; $105.863; $200.057; $506.507; $850.071. Write the following sums in Federal Money: 4. 63 dollars, and 85 cents. 5. 150 dollars, and 73 cents. 6. 201 dollars, and 9 cents. 7. 300 dollars, 5 cents, and 3 mills. Ans. $63.85. 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 76,450 45 dollars. REDUCTION OF FEDERAL MONEY. CASE I.-Reducing Dollars to Cents and Mills. Ex. 1. Reduce 75 dollars to cents and mills. Suggestion.-Since in 1 dollar there are 100 cents, in 75 dollars there are 75 times as many, or 7500 cents. Again, since in 1 cent there are 10 mills, in 7500 cents there are 7500 times as many, or 75000 mills. Now, to multiply by 10, 100, &c., we simply annex as many ciphers to the multiplicand as there are ciphers in the multiplier. (Art. 59.) Hence, Operation. 75 dolls. 100 7500 cts. 10 Ans. 75000 m. QUEST.-207. How do you read Federal Money? Obs. What other mode of reading Federal Money is mentioned? 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 decimal point. Thus, $25.36 reduced to cents, becomes 2536 cents. 2. Reduce 9 cts. to mills. 4. Reduce $5 to cents. 3. Reduce $25 to mills. 5. Reduce $364 to mills. 7. Reduce $6245 to cents. 9. Reduce $625.48 to cents. 6. Reduce $621 to mills. 8. Reduce $75.26 to cents. CASE II.-Reducing Cents and Mills to Dollars. 10. Reduce 45000 mills to dollars and cents. Suggestion. Since 10 mills make 1 cent, 45000 mills will make as many cents as 10. is contained times in 45000, or 4500 cents. Again, since 100 cents make 1 dollar, 4500 cents will make as many dollars as 100 is contained times in 4500, or 45 dollars. Now, to divide by 10, 100, &c., we cut off as many figures from the right of the dividend as there are ciphers in the divisor. (Art. 80.) Hence, Operation. 10)4500|0 mills. 100)4500 cents. Ans. 45 dolis. 209. To reduce cents to dollars, point off two figures on the right. To reduce mills to dollars, point off three figures on the right. 11. Reduce 150 mills to cts. 13. Reduce 325 cts. to dolls. 15. Reduce 4320 m. to dolls. 17. Reduce 4890 mills to cts. 12. Reduce 25000 mills to dolls. 210. Since Federal Money is based upon 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. QST. 208. How are dollars reduced to cents? Dollars to mills? Cents to mi..? Obs. Dollars and cents to cents? lure? Mills to dollars? Mills to cents? off! 29. How are cents reduced to do!Cos. What are the figures pointed 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? Suggestion.-We write the dollars under dollars, cents under cents, &c., and proceed as in addition of decimals. From the right of the amount, we point off three figures for cents and mills. 211. Hence, we derive the following general Operation. $15.75 2.375 3.875 8.68 Ans. $30.680 RULE FOR ADDING FEDERAL MONEY. Write the given numbers under each other, so that dollars may stund under dollars, cents under cents, &c. Begin at the right hand, and adding each column separately point off the amount as in addition of decimals. (Art. 187.) OBs. If either of the given numbers have no cents expressed, 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 a bushel of wheat for $1.12: how much did he receive for the whole? 3. A man bought a hat for $5.375, a cloak for $35.68, and a pair of boots for $4.75: how much did he pay for all? 4. What is the sum of $37.565, $85.20, $90.03, and $150.638? 5. What is the sum of $10.385, $46.238, $190.62, and $23.036? 6. What is the sum of $23.005, $16.03, $110.738, and $131.26? 7. What is the sum of 63 dolls. and 4 cts., 86 dolls. and 10 cts., and 47 dolls. and 37 cts? 8. What is the sum of $608.05, $365.205, $2.268, and $47.006? 9. What is the amount of 11 dolls. 3 cts. and 5 mills, 16 dolls. and 8 mills, 49 dolls. 7 cts. and 8 mills? QUEST.-211. What is the rule for Addition of Federal Money? How point off the amount? Obs. When any of the given numbers have no cents expressed, how is their place supplied? 10. What is the amount of 100 dolls. and 61 cts., 51 dolls. and 3 cts., 65 dolls. 8 cts. and 3 mills? 11. What is the amount of 95 dolls. 67 cts. and 8 mills, 120 dolls. 45 cts., 101 dolls. 7 cts. and 9 mills? 12. A lady bought a bonnet for $6.67, a pair of gloves for $0.625, a pair of shell combs for $0.75,.and a cap for $2.50: what was the amount of her bill? 13. Add $563.871; $19.183; $960.371; $28.061; $806.191. 14. Add 684.071; $493.673; $81.7358; $65.409; $85.0075. 15. Add $8 three cents; 87 cts.; $96 six cents; $9.81. SUBTRACTION OF FEDERAL MONEY. Ex. 1. A man bought a horse for $56.50, and a cow for $23.38: how much more did he pay for his horse than for his cow? Suggestion. We write the less number under the greater, placing dollars under dollars, &c., then subtract, and point off the answer as in subtraction of decimals. 212. Hence, we derive the following general Operation. $56.50 23.38 Ans. $33.12 RULE FOR SUBTRACTING FEDERAL MONEY. Write the less number under the greater, with dollars under dollars, cents under cents, &c. Beginning at the right hand, subtract, and point off the remainder as in subtraction of decimals. (Art. 189.) OBS. If either of the given numbers have no cents expressed, supply their place by ciphers. 2. A man owing $57.35, paid $17.93: how much does he still owe? Ans. $39.42. 3. A grocer bought two hogsheads of molasses for $68.90, and sold it for $79.26: how much did he gain by the bargain? 4. A man owed a debt of $105, and paid but $23.67: how many dollars did he then owe? QUEST.-212. What is the rule for Subtraction of Federal Money? How point off the remainder? Obs. When either of the given numbers has no cents ex pressed, how is their place supplied? |