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101. Parts of a dollar, or any quantity thus expressed, in tenths, hundredths, etc., are termed Decimals, or fractions, whose denominator (Art. 68) is 1, with one or more ciphers annexed. They are usually expressed by simply writing the numerator (Art. 68) with a point (.) before it, called the decimal point, or separatrix; the first place at the right of the point being tenths; the second place, hundredths; the third place, thousandths; the fourth place, ten-thousandths; and so on. Thus, ^ is written .1; TiJff is written .01; J^jj is written .001; Tffiujj is written .0001, etc.
102i In writing dollars and cents together, the decimal point or separatrix is placed between the dollars and the cents or decimal part; and since cents occupy two places, the place of dimes and of cents, when the number of cents is less than 10, a cipher must be written before them, in the place of dimes. Thus, $30,375 is read, thirty dollars thirty-seven cents five mills, or thirty dollars and three hundred seventy-five thousandths of a dollar; $12.05 is read, twelve dollars five cents, or twelve dollars and five hundredths of a dollar, etc.
103i The denominations of United States Money increasing from right to left, and decreasing from left to right, in the same •> manner as do the units of the several orders in simple whole numbers, they may therefore be added, subtracted, multiplied, and divided according to the same rules.
104 i The Coins of the United States are of gold, silver, nickel, and bronze.
The gold coins are the double eagle, eagle, half-eagle, quarter-eagle, three-dollars, and dollar.
The silver coins are the dollar, half-dollar, quarter-dollar, dime, half-dime, and three-eent-piece.
The nicltle coin is a three-cent-piece.
The bronze coins are the cent and two-cent-piece.
Note. — All the gold and silver coins of the United State^ are now made of one parity, 9 parts of pure metal and 1 part alloy. The alloy for the silver ;s copper, and that for the gold 1 part copper and 1 part silver. The cent and two-cent-piece, by the law of 1864, are composed of 95 parts of pure copper and 5 parts of tin and zinc.
The standard weight of the eagle, as fixed by present laws, is 258 grains Troy, and the gold coins in proportion according to their values. The weight of the silver dollar is 412J grains; half-dollar, 192 grains; quarter-dollar, 96 grains; dime 38| grains; half-dime, 19J grains; three-cent piece, 11 grains; the cent, old coinage, 168 grains; the cent, new coinage, 48 grains.
The weight of the silver dollar, it will be seen, is greater in proportion to its value than the other silver coins. This is owing to their standard weight having been reduced, while that of the dollar remained unchanged; but since this reduction of weight of the smaller silver coins, no more of the silver dollar appear to have been coined. In circulation, the gold dollar, which of late years has been extensively coined, has almost entirely taken the place of the silver dollar.
The symbol $, or dollar sign, represents, probably, the letter U written upon au S, denoting U. S. (United States).
KEDTJCTION OF UNITED STATES MONEY.
105. Reduction of United States Money is changing the units of one of its denominations to the units of another, either of a higher or lower denomination, without altering their value.
106i To reduce units from a higher denomination to a lower.
Ex, 1. Reduce 58 dollars to cents and mills.
Ans. 5800 cents; 58000 mills.
5 8 dollars.
100 We multiply the 58 by 100, be
5 8 0 0 cents. cause 100 cents make 1 dollar; and
Q multiply the 5800 by 10, because
. 10 mills make 1 cent. Hence,
Or thus: 5 8 0 0 0 mills.
To "reduce dollars to cents, annex Two ciphers; to reduce dollars to mills, annex Three ciphers; and to reduce cents to mills, annex One cipher.
Xote.—Dollars, cents, and mills, expressed by a single number, are reduced to mills by merely removing the separating point; and dollars and cents, by annexing one cipher and removing the separatrix.
107i To reduce units from a lower denomination to a higher. Ex. 1. Reduce 58000 mills to cents and to dollars.
Ans. 5800 cents; 58 dollars.
10)58000 mills. We divide the 58000 by 10, be
|nn\!jnn „„„ t cause 10 mills make 1 cent: and di
luuioouu cents. ., A, onn , , .'
'vi le the 5800 by 100, because 100
5 8 dollars. cents make 1 dollar. Hence,
To reduce mills to cents, cut off One figure on the right; to reduce cents to dollars, point off Two figures; and to reduce mills to dollars, point off Three figures.
2. Reduce $765 to cents.
3. Change 726 mills to cents. Ans. 72^ cents.
4. How many dollars are 329 cents? Ans. $3.29.
5. Change 12345 mills to dollars. Ans. $ 12.345.
6. Reduce $ 123.56 to mills. Ans. 123560 mills.
7. Reduce 2 eagles, 2 dollars, and 2 dimes to cents.
Ans. 2220 cts.
ADDITION OF UNITED STATES MONEY.
108. Ex. 1. Add together 17 dollars 13 cents 5 mills; 8 dollars 4 cents 6 mills; 63 dollars 20 cents 3 mills; and 29 dollars 87 cents 5 mills. Ans. $ 118.259.
We write units of the same denomination in the same column, and add as in addition of simple numbers (Art. 45), and separate the dollars from the cents in the answer by the decimal point.
Rule.— Write dollars, cents, and mills, so that units of the same denomination shall stand in the same column.
Add as in addition of simple numbers, and place the decimal point directly under that above.
Proof. — The proof is the same as in addition of simple numbers."
6. Add the following sums, $18,165, $701.63, $151,161, $375,089, and $471,017. Ans. $1717.062.
7. Bought a horse for eighty-seven dollars nine cents, a pair of oxen for sixty-five dollars twenty cents, and six gallons of molasses for two dollars six cents five mills; what was the amount of my bill? Ans. $ 154.355.
8. Sold a calf for three dollars eight cents, a bushel of corn for ninety-seven cents five mills, and three bushels of rye for three dollars five cents; what was the amount received?
Ans. $ 7.105.
SUBTRACTION OF UNITED STATES MONEY.
109. Ex. 1. From 106 dollars 7 cents 7 mills, take 92
dollars 83 cents 8 mills. Ans. $ 13.239.
Operation. We write the less number under the
* ct8 m- greater, place mills under mills, cents under
1 0 6.0 7 7 cents, and dollars under dollars, and subtract
9 2.8 3 8 as in subtraction of simple numbers (Art.
A , oaoq 50), and separate the dollars from the cents
Ans. 1 o.Z o » jn answer by tile decimal point.
Rule. — Write the several denominations of the subtrahend under the corresponding ones of the minuend.
Subtract as in subtraction of simple numbers, and place the decimal point directly under that above.
Proof. — The proof is the same as in subtraction of simple numbers.
2. 3. 4. 5.
t cts. m. J cts. m. $ eta. m. $ cts. m
8 7 1.1 6 1 4 7 8.47 7 1 6 7.1 6 3 1 63.1 6 7
8 9.9 1 8 1 9 9.9 9 1 9 8.0 9 7 9.0 9 8
7 8 1.2 43
6. Bought a farm for $1728.90, and sold it for $3786.98; what did I gain by my bargain?
7. Gave $ 79.25 for a horse, and $106,875 for a chaise, and sold them both for $ 200; what did I gain?
8. Bought a farm for $8967, and sold it for nine thousand eight hundred seventy-six dollars seventy-five cents; what did I gain? Ans. $ 909.75.
9. Bought a barrel of flour for $ 7.50, three bushels of rye for $ 2.75, and three cords of wood at $ 5.25 a cord; I sold the flour for $ 6.18, the rye for $ 3.00, and the wood for $ 6.75 a cord; what was gained by the bargain? Ans. $3.43.
10. A young lady went a ''shopping." Her father gave her a twenty-dollar bill. She purchased a dress for $8.16, a muff for $3.19,a pair of gloves for $ 1.12,a pair of shoes for $ 1.90, a fan for $ 0.19, and a bonnet for $ 3.08; how much money did she return to her father? Ans. $ 2.36.
MULTIPLICATION OF UNITED STATES MONEY.
110. Ex.1. What will 365 barrels of flour cost at $ 5.75 a barrel? Ans. $ 2098.75.
$ 5.7 5 We multiply, as in multiplication of sim
3 6 5 pie numbers, and, obtaining the product in
cents, the lowest denomination of the multi
2 8 7 5 plicand, we reduce them to dollars by point
3 4 5 0 ing off two places at the right for cents
1 7 25 (Art. 107).
$2 0 9 8.7 5 Ans.
Rule.—Multiply as in multiplication of simple numbers. The product will be in the lowest denomination in the multiplicand, which must be pointed off as in reduction of United States money.
Proof. — The proof is the. same as in multiplication of simple numbers.
2. What will 126 pounds of butter cost at 13 cents a pound?
3. What will 63 pounds of tea cost at 93 cents a pound?
4. What will 43 tons of hay cost at 13 dollars 75 cents a ton? Ans. $591.25.
5. If 1 pound of pork is worth 7 cents 3 mills, what are 46 pounds worth? Ans. $ 3.358.
6. If 1 hundred of beef cost 3 dollars 28 cents, what are 76 hundred worth?
7. What will 96 thousand feet of boards cost at 11 dollars 67 cents a thousand? Ans. $ 1120.32.
8. If a barrel of cider be sold for 2 dollars 12 cents, what will be the value of 169 barrels? Ans. $ 358.28.