7. What is the product of 8574.3 into 87.5 ? 8. What is the product of 3.973 into 8? 9. What is the product of 49640.54 into .10503 ? 10. What is the product of 7.72 into .294 ? DIVISION OF CIRCULATING DECIMALS. Ex. 1. Divide 234.6 by .1. Operation. 234.6=2343=794 .1=1 Now 794:- =704 x = 36 And 633=301.714285 Ans. We first reduce the divisor and dividend to common fractions; (Art. 358 ;) and divide one by the other; (Art. 229 ;) then reduce the quotient to a decimal. (Art. 337.) Hence, 365. We derive the following general RULE FOR DIVIDING CIRCULATING DECIMALS. Reduce the divisor and dividend to common fractions ; divide one fraction by the other, and reduce the quotient to decimals. OBs. After the divisor is inverted, if the numerators and denominators have factors common to both, the operation may be contracted by canceling those factors. (Art. 232.) 2. Divide 319.28007112 by 764.5. Ans. 0.4176325. 9. Divide 24.08i by .386. 10. Divide .36 by .25. SECTION XI. FEDERAL MONEY. ART. 366. FEDERAL MONEY is the currency of the United States. Its denominations, we have seen, are Eagles, Dollars, Dimes, Cents, and Mills. (Art. 244.) 367. All accounts in the United States are required by law to be kept in dollars, cents, and mills. Eagles are expressed in dollars, and dimes in cents. Thus, instead of 8 eagles, we say, 80 dollars; instead of 6 dimes and 7 cents, we say, 67 cents, &c. 368. Federal Money is based upon the Decimal system of Notation. Its denominations increase and decrease from right to left and left to right in a tenfold ratio, like whole numbers and decimals. (Art. 244. Obs. 1.) 369. 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 are distinguished from whole numbers. (Art. 311.) 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. 313.) For example, 4 cents are written thus .04; 9 cents thus .07; &c. 2. Mills occupy the third place of decimals; for they are thousandths of a dollar. Consequently, when there are no cents in the given sum, two ciphers must be placed before the mills. Hence, QUEST.–366. What is Federal Money ? 367. In what are accounts kept in the U. S. ? How would you express 8 eagles ? How express 6 dimes and 7 cents ? 368. Upon what is Federal Money based ? 369. What is regarded as the unit in Federal Money? What are cents and mills? How are they distinguished from dollars ? 370. 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 third figure denotes mills ; the other places on the right are decimals of a mill. Thus, $3.25232 iş 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." Write the following sums in Federal money : 1. 70 dollars, and 8 cents. Ans. $70.08. 2. 150 dollars, 3 cents, and 5 mills. 3. 409 dollars, 40 cents, and 3 mills. 4. 200 dollars, 5 cents, and 2 mills. 5. 4050 dollars, 65 cents, and 3 mills. Note.-In business transactions, when dollars and cents are expressed to gether, the cents are frequently written in the form of a common fraction. Thus, the sum of $75.45, is written 751 dollars. REDUCTION OF FEDERAL MONEY. CASE I. Ex. 1. How many cents are there in 95 dollars ? Solution.-Since in 1 dollar there are 100 cents, in 95 dollars there are 95 times as many. And 95X100=9500. Ans. 9500 cents. 2. In 20 cents how many Ans. 200 mills. Note.—To multiply by 10, 100, &c., we simply annex as many ciphers to the multiplicand, as there are ciphers in the multiplier. (Art. 99.) Hence, 371. 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, cents, and mills, to mills, erase the sign of dollars and the separatrix. Thus, $25.36 reduced to cents, becomes 2536 cents. Quest.–370. How do you read Federal Money? Obs. What other mode of reading Federal Money is mentioned ? 371. How are dollars reduced to cents ? Dollars to mills ? Cents to mills ? Obs. Dollars, cents, and mills, to mills ? Ans. 1200 cents, 3. In $12 how many cents ? 4. In $460 how many cents ? 5. In $95 how many mills ? 6. In 90 cents how many mills ? 7. Reduce $25.15 to cents. 8. Reduce $864.08 to cents. 9. Reduce $1265.05 to mills. 10. Reduce $4580.10 to mills. 11. Reduce $6886.258 to mills. 12. Reduce $85625.40 to mills. CASE II. 13. In 6400 cents, how many dollars ? Suggestion.—Since 100 cents make 1 dollar, 6400 cents will make as many dollars as 100 is contained times in 6400. And 6400-100=64. Ans. $64. 14. In 260 mills, how many cents ? Ans. 26 cents. Note.-To divide by 10, 100, &c., we simply cut off as many figures from the right of the dividend as there are ciphers in the divisor. (Art. 131.) Hence, 372. To reduce cents to dollars, cut off two figures on the right. To reduce mills to dollars, cut off three figures on the right. many dollars ? Ans. $6.26. 16. In 1516 cents, how many dollars ? 17. In 162 mills, how many cents ? 18. In 1000 mills, how many dollars ? 19. In 2360 mills, how many cents ? 20. In 3280 mills, how many dollars ? 21. Reduce 8500 cents to dollars. 22. Reduce 2345 cents to dollars, &c. 23. Reduce 92355 mills to dollars, &c. QUEST.-372 How are cents reduced to dollars ? Mills to dollars ? Mills to cents ! Obe. What are the figures cut off ? 24. Reduce 150233 mills to dollars, &c. 25. Reduce 450341 cents to dollars, &c. 373. 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 cloak for $35.375, a hat for $4.875, a pair of boots for $6.50, and a coat for $23.625 : what did he pay for all ? Operation. $35.375 4.875 6.50 23.625 $70.375 Ans. We write the dollars under dollars, cents under cents, &c. Then add each column separately, and point off as many figures for cents and mills, in the amount, as there are places of cents and mills in either of the given numbers. Hence, 374. We derive the following general RULE FOR ADDING FEDERAL MONEY. Write dollars under dollars, cents under cents, &c., so that the same orders or denominations may stand under each other. Add each column separately, and point of the amount as in addition of decimal fractions. (Art. 320.) Oes. If either of the given numbers have no cents expressed, it is customary to supply their place by ciphers. 2. What is the sum of $48.25, $95.60, $40.09, and $81.10 ? 3. What is the sum of $103.40, $68.253, $89.455, $140.02, and $180 ? 4. What is the sum of $136.255, $10.30, $248.50, $65.38, and $100.125 ? QUEST.–374. 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 ? |