decimal is required, and divide as in Case 3d; the quotient will be the decimal required. Note. If there are not so many places in the quotient as there were ciphers annexed, supply the defect by prefixing ciphers. EXAMPLES. 1. Reduce 1 farthing to the decimal of a pound. 2. Reduce 2 and 3 farthings to the decimals of a pound. ,00208+,003125 Ans. 3. Reduce 1, 2 and 3 farthings to the decimals of a shilling. ,0208+,0416+,0625 Ans. 4. Reduce 1, 2 and 3 farthings to the decimals of a penny. ,25,5,75 Ans. 5. Reduce from 1 to 11 pence to the decimals of a pound. ,00416+,00833+,0125 0166+,0208+,025 7. 8. 9. 10. ,02916,0333+,0375 ,0416+,0458 6. Reduce from 1 to 11 pence to the decimals of a shilling, Note. ,583+,666+,75 When shillings are to be reduced to the decimal of a pound, if the shillings be an even number, half the number, with a comma prefixed, is the decimal; but if the number be uneven annex a cipher to it, and then halve it as before. EXAMPLES. 77. Reduce from 1 to 19 shillings to the decimals of a pound. 8 9 10 shillings. 2 3 4 5 6 ,5 decimals. 11 12 13 14 15 16 17 18 955 ,6,65 ,7,75 ,8,85 3. Reduce 3 pwts, to the decimal of a pound Troy. 19 shillings. ,95 decimals. ,0125 Ans 9. Reduce 4 ounces to the decimal of a lb. Avoirdupois. 10. 11. ,25 Ans. ,0625 Ans. Reduce 7lb. to the decimal of 1 cwt. Reduce 3 inches to the decimal of a yd.,0833+Ans. 12. Reduce 8 inches to the decimal of a ft. ,666+Ans. 13. Reduce 10 inches to the decimal of a mile. ,0001578 Ans. 14. Reduce 8 yds. to the decimal of a mile. ,004545+Ans. 15. Reduce 15 minutes to the decimal of an hour.,25 Ans. 16. Reduce 18 hours to the decimal of a day. 17. Reduce 65 days to the decimal of a year. ,75 Ans. 178+Ans. CASE V. To find the true value of any decimal, whether of coin, weight, or measure. RULE. Multiply the given decimal by so many of the next lower denomination, as make one in that denomination of which the given decimal is a part; then point off so many places from the right hand of the product as there are places in the given decimal; the left hand figures are whole numbers; then multiply the figures which were pointed off, by the parts of the next lower denomination, and point off as before; thus proceed through every descending denomination; the figures at the left hand of the several products determine the value of the decimal. EXAMPLES. 1. What is the value of,5956 of a pound? 2. What is the value of,384 of a shilling? 4 d. Ans. 3. What is the value of,9345 of a pound Troy? 11oz. 4pwt. 6gr. Ans. 4. What is the value of ,75254 of a mile ? 240 rods. 4 yds. 1 ft. 5. What is the value of ,857 of a day? What is the value of,75 of a year? 4 in. 2 bar Ans. 20h. 84m. 4s. Ans. 273d. 18h. Ans. DUODECIMALS. DUODECIMALS is a rule, which of all others, if accurately understood, is the most expeditious for finding the contents of boards, timber, or cord wood. This rule is called Duodecimals, because every inferior denomination decreases in a twelve-fold proportion. Dimensions are commonly given in feet, inches, and parts of an inch. RULE 1. Place feet under feet; inches under inches, &c. RULE 2. Having properly stated the question, begin with the highest denomination of the multiplier, (that is feet) and multiply it crosswise into the lowest denomination of the multiplicand, observing, in every denomination, to carry one for every twelve. RULE S. Having multiplied every denomination of the multiplicand, by the feet, in the multiplier, begin with the inches, in the multiplier, and proceed as in the first instance, observing to set the first figure of the product one place to the right hand of the first product; thus proceed with every succeeding denomination. RULE 4. Add the several products together, their sum will be the answer required. In the first example, I begin with the feet, in the multiplier, and multiply them into the inches of the multiplicand, thus; 2 times 8 are 16, which is one foot, four inches; I set down 4, and then say, two times 3 are 6, and one I carry are 7, which I set down. I then proceed to multiply the inches in the multiplier, into the inches of the multiplicand, and set the first figure of the product, one place to the right hand of the first figure, in the first product. Lastly, I add the two products together, and find the amount to be 7 feet, 11 inches, and 4 twelfths of an inch; or, in other words, 7 feet, 11 twelfths of a foot, and 4 twelfths of an inch. -Note. The inferior denominations below feet are sometimes called primes, seconds, thirds, &c. and are thus marked: primes ()seconds (") thirds (") &c. SUPERFICIAL MEASURE is that which considers length and breadth, without regard to thickness. 3. How many feet in a board 10 feet, 7 inches long, and 9 inches wide? 7: 11' 3' Ans. 4. How many feet in a floor 10 feet, 8 inches wide, and 11 feet, 9 inches long? 125 4' Ans. 5. How many feet in a board, 9 feet, 6 inches and a quarter long, and 5 inches and a half wide? 4: 4' 4": 4": 6" Ans. Note. When the length of a board or stick of timber, exceeds twelve feet, or any number of times twelve, find the contents of twelve feet in length, in the first place; then multiply the contents of twelve feet in length, by as many as there are twelves in the length of the board, or timber: then, by a separate operation, find the contents of the overplus, (if there be any,) and add it to the contents of the even twelve, or twelves; their sum will be the contents of the whole length. EXAMPLES. 1. How many feet in a board 18 feet, 7 inches long, and 14 inches wide? 2. How many feet in a board 27 feet, 8 inches long, and 11 inches wide? 3. 8 Overplus of 24 feet. 0 11 Width. 3 : 4 4 Con. of overplus, 25 4 4 Con. of 27 ft. 8 in. Ans. How many feet in a board, 38 feet, 10 inches long, and 13 inches wide? 42 0' 10' Ans. 4. How many feet in a board 19 feet, 51⁄2 inches long, and 10 inches wide? 17: 0' 3" : 9"" Ans. Note. Painting and some other kinds of work, are done by the square yard; and, in order to find how many square yards any piece of work contains, find how many feet there are by the foregoing rules; then divide the feet by 9, and the quotient will be the number of square yards. 3. Agreed to have several pieces of work painted, at 20 cents per square yard. What will the whole amount to, the several pieces being of the following dimensions? CUBIC, or SOLID MEASURE, is that, which considers length, breadth, and thickness. |