DECIMAL FRACTIONS Are such as have a unit for their denominator, with as many ciphers annexed as there are figures in the numerators; as,, usually written with a point prefixed without the denominator •2, 34, 564, and read thus: 2, two tenths; 34, thirty-four hundredth parts; 564, five hundred and sixty-four thousand parts; and so on. NOTE. Ciphers on the right hand of decimals do not alter their value. REDUCTION OF DECIMALS. PROB. 1. To reduce a vulgar fraction to a decimal. RULE. Annex ciphers to the numerator, and divide by the denominator. 1. What is the decimal of 1, 2, and 2? Ans. •25, 5, 75. 2. Reduce to a decimal. Ans. 6. 3. What is the decimal of? 4. Reduce to a decimal. 5. What is the decimal of? Ans. 125. Ans. ·375. Ans. 625. Ans. 5834. Ans. ·34094. 8. What is the decimal of? Ans. 098116. NOTE. If there are not as many figures in the quotient as ciphers annexed, supply the defect by writing ciphers on the left hand. PROB. 2. If the given number consists of several denominations. RULE. Reduce it to the lowest denomination for a numerator, and reduce the denominator to the same; then annex ciphers, and divide as before. Or: Begin at the lowest, and reduce them in their order. 1. Reduce 15s. 6d. to the decimal of a pound. Ans. 7781252 2. Reduce 9d. to the decimal of a pound. Ans. ⚫03751. 3. Reduce 8s. 6d. to the decimal of a pound. Ans. 4251. 4. Reduce 12s. 84d. to the decimal of a guinea. Ans. 605158736. 5. Reduce 6 d. to the decimal of a shilling. Ans. •541632. 6. Reduce 8 oz. 12 dwt. 16 gr. to the decimal of a lb. troy. Ans. 719444256 7. Reduce 2 qr. 16 lb. to the decimal of a cwt. Ans. 64285716. 8. Reduce 20 yds. 2 f. 6 in. to the decimal of a mile. Ans. ·01183711344. 9. Reduce 2 qr. 2 al. to the decimal of a yard. Ans. 625. 10. Reduce 1 rood, 20 po. to the decimal of an acre. Ans. 375. 11. Reduce 3 bush. 1 pk. to the decimal of a quarter. Ans. 40625. 12. Reduce 15 gallons of wine to the decimal of 252 gallons. Ans. ·059523824. 13. Reduce 63 inches to the decimal of a foot. Ans. 5625. PROB. 3. To find the value of a decimal. RULE. Multiply it by the value of the given denomination, and point off as many decimals from the right hand of the product as there are places in the given decimal. The figures on the left hand are integers of the next lower denomination; reduce the figures pointed off into the next lower denomination; proceed in this manner till you come to the lowest. 1. What is the value of 85 of a £? 2. What is the value of 1875l.? 3. What is the value of 125s.? 4. What is the value of 20 lb. 10 oz. 9 dr. 984. Ans. 17s. Ans. 3s. 9d. Ans. 1d. 6845 cwt.? Ans. 2 qr. 5. What is the value of 121 of 252 gallons? Ans. 30 gal. 1 qt. 1 pt. 936. 6. What is the value of 03125 of 36 gallons? Ans. 1 gal. 1 pt. 7. What is the value of 28 of a mile? Ans. 2 fur. 9 po. 3 yds. 10 in. 80. PROB. 4. To find the decimal of Sterling money by inspection. RULE. Take half the even number of shillings for the first decimal figure; and the number of farthings in the remainder, increased by 1, if they amount to 24, or upwards; by 2, if they amount to 48, or upwards; and by 3, if they amount to 72, or upwards, for the second and third figures; if there is but one figure, prefix a cipher to it. To complete the decimal, call these two figures or their excess above 25, 50, or 75, pence; the farthings in them increased by 1 for every 24, give other two figures; continue this method till the decimal ends or repeats. 1. Reduce 6s. 44d. to the decimal of a pound. Ans. 318751. 2. Reduce 9s. 6d. to the decimal of a pound. Ans. 4781257. 3. Find by inspection the decimal of 10s. 84d. Ans. 5343751. 4. Reduce 12s. 7 d. to the decimal of a pound. Ans. 63229167. 5. Reduce 16s. 114d. to the decimal of a pound. Ans. 8468751. 6. Reduce 19s. 11 d. to the decimal of a pound. Ans. 99895831. PROB. 5. To value the decimal of a pound Sterling by inspection. RULE. Double the figure next the point for shillings, if the next figure is 5, or upwards, take 5 from it, and add 1 to the shillings; then the second and third figures are farthings, after deducting 1 for every 25 in them. RULE. Write down the given numbers, placing the deci mal points directly under each other; then proceed as in whole numbers. ADDITION. 1. What is the sum of 2-64, 85.6, 945, 14.8, 5.3456, and 84? Ans. 193-3306. 2. What is the sum of 785-1, 84.35, 1.654, •8956, 009, and 10-161? Ans. 882.1696. 3. What is the sum of 25-3, 2-78, 324-67, 1-294, 63.14, and 345-6? Ans. 762.784. 4. What is the sum of 325-7, 63.451, 275-34, 6.473, 25.68, and 287-435? Ans. 984-079. 5. What is the sum of 3285-64, 287-458, 4550-67, 38-4526, 324-578, and 4761-29? Ans. 13248-0886. SUBTRACTION. 1. What is the difference between 8406 and •58975? Ans. •25085. 2. What is the difference of 84.95 and 3.6954? Ans. 81.2546. 3. What is the difference of 246 and 8154? Ans. 245 1846. 4. L borrowed from M 20-781257. and afterwards paid him 147. 18s. 9d. What remains due to M? Ans. 5l. 16s. 10дd. 5. Find the difference between 40 yards, 2 quarters, and 29.625 yards? Ans. 10 yds. 3 qr. 2 nl. MULTIPLICATION OF DECIMALS. RULE 1. Place the factors, and multiply as in whole num. bers. 2. Point off as many decimal places in the product towards the right hand as there are in both factors; and if the product has not so many, supply the defect by writing ciphers on the left hand. 1. Multiply 346.549 by 3·15. Ans. 1091-62935. 2. Multiply 516-8945 by 44-89. Ans. 23203-394105. 3. Multiply 84615 by 065. Ans. ·05499975. 4. Multiply 346809 by 00546. Ans. 00189357714. 5. A gentleman has ·831257. a-day, how much is that a-year? Ans. 303l. 8s. 11⁄2d. DIVISION OF DECIMALS. RULE. Divide as in whole numbers, and point off as many decimal places in the quotient as the dividend has more than the divisor. NOTE 1. If there are not as many decimal places in the quotient as required, supply the defect by writing ciphers on the left hand. 2. If there is a remainder, the quotient may be carried to any degree of exactness by annexing ciphers; or, if the decimal places in the divisor are more than those in the dividend, ciphers may be annexed to the dividend. 3. If the dividend will not contain the divisor, annex ciphers, or suppose them to be annexed, to the dividend. Ans. 7.35. Ans. 12·32120, 1. Divide 176·4 by 24. 2. Divide 45-3496 by 3.68. 3. Divide 24-694 by 45. 4. Divide 8496 by ⚫546. 5. Divide 21468 by 2.5. 6. Divide 80468 by 075. 7. Divide 8.4567 by 25. 8. Divide ·06548 by 215. 9. Divide 216-4 by 100. 10. A merchant bought a cwt. of sugar for 3.851. and intends to gain 14d. on each lb., at what rate must he retail it per lb.? Ans. 9 d. Ans. 0003098. |