For since dollar is the money unit; and a dime being the tenth, a cent the hundredth, and a mill the thousandth part of a dollar, or unit, it is evident that any number of dollars, dimes, cents and mills, is simply the expression of dollars, and decimal parts of a dollar : Thus, 11 dollars, 6 dimes, 5 cents,=11,65 or 11 dol. &c. 3. Add the following mixed numbers together. (2) (3) (4) Yards. Ounces. Dollars. 46,23456 12,3456 48,9:08 24,00400 7,871 1,8191 17,00411 2,34 3,1030 3,01111 5,6 7012 5. Add the following sums of dollars together, viz. $12,34565+7,891+2,34+14, +0011. Ans. $36,57775, or $36, 5di. 7cts. 77. mills. 6. Add the following parts of an acre together, viz. ,7569+,25+,654+199 Ans. 1,8599 acres. 7. Add 72,5+32071 +2,1574+371,4+2,75 Ans. 460,8784. 8. Add 30,07+200,71 +59,4+3207,1 Ans. 3497,28. 9. Add 71,467+27,94-16,094-98,009—86,5 Ans. 300. 10. Add ,7509-0074,694,8408-,6109 Ans. 2,9 11. Add ,6,099,37-,905,026 Ans. 2 12. To 9,999999 add one millionth part of an unit, and the sum will be 10. 13. Find the sum of Twenty-five hundredths, Three hundred and sixty-five thousandthis, $ix tenths, and nine millionths, Answer, 1,215009 SUBTRACTION OF DECIMALS. RULE Place the numbers according to their value; then subtract as in whole numbers, and point off the decimala as in addition. 6. From 480 take 245,0075 Ans. 234,9925 7. From 236 dols. take ,549 dols. Ans. $235,451 8. From ,145 take ,09684 Ans. ,04816 9. From ,2754 take ,2371 Ans. ,0383 10. From 271 take 215,7 Ans. 55,3 11. From 270,2 take 75, 4075 Ans. 194,7925 12. From 107 take ,0007 Ans. 106,9993 13. From a unit, or 1, subtract the millionth part of itself, Ans. ,999999 MULTIPLICATION OF DECIMALS. RULE 1. Wliether they be mixed numbers, or pure decimals, place the factors and multiply them as in whole numbers. 2. Point off so many figures from the product as there are decimal places in both the factors ; and if there be not so many places in the product, supply the defect by prefixing cyphers to the left hand. EXAMPLES. 1. Multiply 5,236 by ,008 2. Multiply 3,024 by 2,23 Product, ,041888 6,74352 3. Multiply 25,238 by 12,17 Answers, 307,14646 4. Multiply 2461 by ,0529 130,1869 5. Multiply 7853 by 3,5 27485,5 6. Multiply ,007853 by ,035 ,000274855 7. Multiply 004 by ,004 ,000016 8. What cost 6,21 yards of cloth, at 2 dols. 32 cents, 5 mills per yard? Ans. $14, 4d. 3c. 8,77 m. 9. Multiply 7,02 dollars by 5,37 dollars. Ans. 36,9954 dols. or $36 99cts, 54 m. 10. Multiply 41 dols. 25 cts. by 120 dollars. Ans. $4950, 11. Multiply 3 dols. 45 cts. by 16 cts. Ans. $0,5520=55cts. 2mills. 12. Multiply 60 cents by ,09 or 9 cents. Ans. $0,0585=5ctş. 8 mills. 13. Multiply 10 dols, by 10 cts. 14. Multiply 341,45 dols. by ,007 or 7 mills. Ans. $2,39 To multiply by 10, 100, 1000, &c. remove the sepa, rating point so many places to the right hand, as the multiplier has ciphers. Multiplied by 10, makes 4,25 So ,425 by 100, makes 42,5 by 1000, is ,425 For ,425 X 10 is 4,250, &c. Ans. $1. DIVISION OF DECIMALS. RULE. 1. The places of the decimal parts of the divisor and quotiënt counted together, must always be equal to those in the dividead, therefore divide as in whole numbers, and from the right hand of the quotient, point off so many places for decimals, as the decimal places in the dividend exceed those in the divisor. 2. If the places in the quotient be not so many as the ruhe requires, supply the defect by prefixing, cyphers to the left hand of said quotient. Note.--If the decimal places in the divisor be more than those in the dividend, annex as many cyphers to the dividend as you please, so as to make it equal, (at least) to the divisor. Or, if there be a remainder, you may annex cyphers to it, and carry on the quotient to any degree of exactness. 00 00 3. Divide 780,517 by 24,3 Anwers. 32,12 4. Divide 1,18 by ,1812 ,23068+ 5. Divide 7,25406 by 957 ,00758 6. Divide ,00078759 by ,525 ,00150+ 7. Divide 14 by 365. ,038356-7 8. Divide $246,1476 by $604,25 ,40736+ • 9. Divide *186513,239 by $304,81 611,9+ 10. Divide $1,28 by $8,31 ,154 + 11. Divide 56 cts. by 1 dol. 12 cts. ,5 12. Divide 1 dollar by 12 cents, 8,333+ 13. If 21 or 21,75 yards of cloth cost 34,317 dollars, what will one yard cost? $1,577 Note.-Then decimals, or whole numbers, are to be divided by 10, 100, 1000, &c. (viz. unity with cyphers, it is performed by removing the separatrix in the dividend, so many places towards the left hand as there are èyphers in the divisor. EXAMPLES. 572 divided by 10, the quotient, is 57,2 5,72 1000, ,572 100, REDUCTION OF DECIMALS. CASE.I. To reduce a Vulgar Fraction to its equivalent Decimal. RULE. Annex cyphers to the numerator, and divide by the denominator ; and the quotient will be the decimal required. Note. So many cyphers as you annex to the given numerator, so many places must be pointed in the quotient; and if there be not so many places of figures in the quotient, make up the deficiency by placing cyphers to the left hand of the said quotient. EXAMPLES. 1. Reduce $ to a deaimal. 8)1,000 ,75 Ans. ,125 2. What decimal is equal to $? Answers. ,5 3. What decimal is equal to *? 4. Reduce } to a decimal. 5. Reduce H to a decimal. ,6875 6. Reduce 17. to a decimal. ,85 7. Bring to a decimal. ,09375 8. What decimal is equal to złę? ,037037+ 9. Reduce to a decimal. 333333+ 10. Reduce 1125 to its equivalent ecimal. ,009 Il. Reduce ye to a decimal. 1923076? |