U mon fraction, and we have £. (Art. 165.) Now reduced to a decimal is £.375. Ans. Hence, 200. To reduce a compound number to the decimal of a higher denomination. First reduce the given compound number to a common fraction; (Art. 165;) then reduce the common fraction to a decimal. (Art. 197.) 2. Reduce 5s. 4d. to the decimal of £1. Ans. £.2666+. 3. Reduce 15s. 6d. to the decimal of £1. 4. Reduce 12s. 6d. to the decimal of £1. 5. Reduce 9d. to the decimal of 1 shilling. 6. Reduce 7d. 2 far. to the decimal of a shilling. 7. Reduce 1 pt. to the decimal of a quart. 8. Reduce 18 hours to the decimal of a day. 9. Reduce 9 in. to the decimal of a yard. 10. Reduce 2 ft. 6 in. to the decimal of a yard. 11. Reduce 6 furlongs to the decimal of a mile. 12. Reduce 13 oz. 8 dr. to the decimal of a pound. CASE IV. Ex. 1. Reduce £.123 to shillings, pence, and farthings. Operation. 20 shil 2.460 12 pence 5.520 4 Multiply the given decimal by 20, as if it were a whole pound, because 20s. make £1, and point off as many figures for decimals as there are decimal places in the multiplier and multiplicand. (Art. 191.) The product is in shillings and a decimal of a shilling. Then multiply the decimal of a shilling by 12, and point off as before, &c. The numbers on the left of the decimals, Ans. 2s. 5d. 2 f. viz: 2s. 5d. 2 far. form the answer. 2.080 Hence, QUEST.-200. How is a compound number reduced to the decimal of a higher denomination? 201. To reduce a decimal compound number to whole numbers of lower denominations. Multiply the given decimal by that number which it takes of the next lower denomination to make ONE of this higher, as in reduction, (Art. 161, I,) and point off the product, as in multiplication of decimal fractions. (Art. 191.) Proceed in this manner with the decimal figures of each succeeding product, and the numbers on the left of the decimal point in the several products, will constitute the whole number required. 2. Reduce £.125 to shillings and pence. Ans. 2s. 6d. 6. Reduce .6254 days to hours, minutes, and seconds. 8. Reduce .6945 of a ton to hundreds, &c. FEDERAL MONEY.. 202. FEDERAL MONEY is the currency of the United States. The denominations are, Eagles, Dollars, Dimes, Cents, and Mills. OBS. Federal Money was established by Congress, Aug. 8th, 1786. Previous to this, English or sterling money was the principal currency of the country. QUEST.-201, How are decimal compound numbers reduced to whole ones ? 202. What is Federal Money? Recite the Table. Obs. When and by whom was it established? 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 28th 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 258 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 412 grains of standard silver; the others, like proportions. 3. The copper coins are the cent, and half cent. The cent contains 168 grains of pure copper; 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 commonly 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, 19 carats fine; and when absolutely pure, it is 24 carats fine.* 2. The present standard for both gold and silver coins of the United States, by Act of Congress, 1837, is 900 parts of pure metal by weight to 100 parts of alloy. The alloy of gold coin is composed of silver and copper, the silver not to exceed the copper in weight. The alloy of silver coin is pure copper. 204. All accounts in the United States are kept in 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? What is the standard for the gold and silver coins of the United States? What is the alloy of gold coins? What of 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. dollars, cents, and mills. 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 Federal Money is based upon the Decimal system of Notation; that its denominations increase and decrease from right to left and left to right in a tenfold ratio, like whole numbers and decimals. 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.) Dollars 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 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 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 thou sandths of a dollar. Consequently, when there are no cents in the given sum, two ciphers must be placed before the mills. Hence, 207. To read any sum of Federal Money. Call all the figures on the left of the decimal point dol lars; the first two figures after the point, are cents; the QUEST.-205. How do the denominations of Federal Money increase and decrease? Upon what is it based? 206. What is regarded as the unit in Federal Money? What are cents and mills? How are they distinguished from dollars? 207. How do you read Federal Money? Obs. 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." 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 76-45 dollars. REDUCTION OF FEDERAL MONEY. CASE I. 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. 7500. And 75×100= Ans. 7500 cents. Ans. 90 mills. 2. In 9 cents, how many mills? 3. In 25 dollars, how many mills? Ans. 25000 mills. |