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176. A Denominate Number is a number composed of one or more units of any denomination, and may be simple or compound.
A simple denominate number is a number composed of but one denomination.
Thus, 7 miles; 6 hours; 5 tons.
A compound denominate number is a number composed of two or more denominations of the same
Thus, 10 lb. 6 oz.; 6 yr. 3 mo.
177. Reduction is the process of changing a number from one denomination to another without altering its value.
A number is changed to a lower denomination when it is changed to a denomination of less unit value. Thus, $1 = 10 dimes 100 cents.
A number is changed to a higher denomination when it is changed to a denomination of greater unit value.
Most of the tables in Denominate Numbers except those in the Metric System are based on varying scales.
The only other tables that are not based on a varying scale are the table of counting 12 things make 1 dozen, 12 dozen 1 gross, 12 gross 1 great gross, etc., based on the duodecimal scale; the table of United States Currency, and some of the tables of Foreign Currency, based on the decimal scale.
I. CANADA MONEY.
178. The currency of the Dominion of Canada is decimal, and the table and denominations are the same as those of United States money.
1. The currency of the whole Dominion of Canada was made uniform July 1, 1871. Before the adoption of the decimal system, pounds, shillings, and pence were used.
2. The silver coins are the 50 cent piece, 25 cent piece, 10 cent piece, and 5 cent piece. The bronze coin is the cent.
3. The gold coin used in Canada is the British Sovereign, worth $4.863, and the Half-Sovereign.
II. ENGLISH MONEY.
179. English Currency is the currency of Great Britain. The unit is the pound sterling.
1. Farthings are generally expressed as fractions of a penny; thus 1 far., sometimes called 1 quarter (qr.), = }d.; 3 far. = }d.
2. The gold coins are the sovereign (= £1), and the half-sovereign.
3. The silver coins are the crown (= 58.), the half-crown (= 2s. 6d.), the florin (= 28.), the shilling, and the sixpenny, fourpenny, and threepenny pieces. 4. The copper coins are the penny, halfpenny, and farthing.
5. The guinea (=218.) and the half-guinea (=10s. 6d. sterling) are old gold coins, and are no longer coined.
III. FRENCH MONEY.
180. The currency of France is decimal currency. The unit is the franc (about 20 cents U. S. money) of which the other denominations are divisors.
* For table of U. S. Currency, see § 158.
10 millimes make 1 centime. 100 centimes 66 1 franc.
COINS.-1. The gold coins are the 40, 20, 10, and 5 franc pieces. 2. The silver coins are the 5, 2, and 1 franc, the 50 and 20 centime pieces. 3. The bronze coins are the 10, 5, 2, and 1 centime pieces.
IV. GERMAN MONEY.
181. The currency of Germany is decimal money. The unit is the mark of 100 pfennige, about 24 cents.
COINS.-1. The gold coins are the 5, 10, and 20 mark pieces.
2. The silver coins are the 20 pfennig, 1 and 2 mark pieces.
3. The nickel coins are the 5 and 10 pfennig pieces.
182. To change a compound denominate number to a lower denomination.
1. Reduce £21 18s. 10d. 2 far. to farthings.
RULE. I. MULTIPLY the highest denomination of the given number by that number of the scale which will reduce it to the next lower denomination, adding to the product the given number, if any, of that lower denomination.
II. Proceed in the same manner with the results obtained in each lower denomination, until the reduction is brought to the denomination required.
PRAC. AR.- -11
183. To change a compound denominate number to a higher denomination.
1. Reduce 21066 farthings to pounds.
12 5266d. + 2 far. 210 43 88.+ 10d.
Ans. £21 18s. 10d. 2 far.
divide 4388. by 20, and we find that 4388.£21+188. The last quotient with the several remainders annexed in the order of the succeeding denominations, gives the answer £21 18s. 10d. 2 far.
I. DIVIDE the given number by that number of the scale which will reduce it to the next higher denomi nation.
II. Divide the quotient by the next higher number in the scale; and so proceed to the highest denomination required. The last quotient, with the several remainders annexed in a reversed order, will be the answer.
Reduction to lower denominations and reduction to higher denominations mutually prove each other.
2. In 14194 farthings how many pounds are there? 3. In £14 15s. 8d. 2 far. how many farthings are there?
4. In 15359 farthings how many pounds are there? 5. In 46 sov. 12s. 2d. how many pence are there? 6. In 11186 pence how many sovereigns are there? 7. In 40 francs how many centimes are there? 8. In 20 mark how many pfennige are there? 9. In 1000 centimes how many francs are there? 10. In 2000 pfennige how many mark are there? 11. In 1624 pence how many pounds are there? 12. How many centimes are there in 22 francs?
MEASURES OF WEIGHT.
184. Weight is the measure of gravity, and varies according to the quantity of matter a body contains. The scales of weight in common use in the United States are the Troy and Avoirdupois.
STANDARD OF WEIGHT.
185. In the year 1834 the United States government adopted a uniform standard of weights and measures, for the use of the custom-houses, and the other branches of business connected with the general government.
The United States standard unit of weight is the Troy pound of the mint, which is the same as the imperial standard pound of Great Britain. A cubic inch of distilled water weighed in a vacuum at 62° Fahrenheit weighs 252.458 grains, and the standard Troy pound contains 5760 such grains.
The United States Avoirdupois pound is determined from the standard Troy pound, and contains 7000 Troy grains.
186. Troy Weight is used in weighing gold, silver, and jewels and in philosophical experiments.
In weighing diamonds, pearls, and other jewels, the unit commonly employed is the carat, equal to 4 carat grains or 3.168 troy grains. The term carat is also used to express the number of parts in 24 that are pure gold. Thus gold that is 12 carats fine is pure gold and alloy.