4)300 75 Here two cyphers must be added to the nume rator, which divided by 4 quotes 75, which I mark for decimals, as there are two decimals added to the dividend, and the quotient is the feventy-five hundredth part of a pound, or, equal to 155. Example 2. What is the decimal fraction of a pound equal to gd.?-Anf. .0375. As there are but three places of figures 24,0)90000 (.0375 in the quotient, I place a cypher on the left thereof, for there fhould be four figures pointed off for decimals, being fo many cyphers annexed to 93 thus the quotient is of a pound. Example 3. What is the decimal fraction of a pound for 3 farthings-Auf. .003125. Here the vulgar fraction for 3 96,0)300000,0(.003125 farthings is; I therefore place as many cyphers as are neceffary to the numerator 3, which in this cafe is 6 cyphers, and the quotient is 3125, but there must be 6 decimals in the quotient, as there are 6 in the dividend and none in the divifor; I therefore prefix two cyphers to the left hand thereof as before directed. Example 4. What is the decimal fraction of a year for 73 days?-Anfwer.2, equal to 5 365)730(.2 Cafe 2. To find the value of a decimal fraction in money, weight, or measure. Rule. Multiply the decimal fraction by the number of parts of the next inferior denomination, and from the product cut off as many figures from the right hand fide as there are decimal places in the fraction. Then multiply thefe figures fo feparated on the right hand by the number of parts of the next inferior denomination, and from the product cut off as many figures as this laft multiplicand has decimal places, as befere. Proceed in the fame manner through all the denominations, then the feparated figures on the left hand side will be the answer. Example Example 1. What is the value of .564 of a pound sterling? ,564 20 fhillings in a pound 11,280 12 pence in a fhilling 3,360 4 farthings in a penny 1,440 Answer 11s. 3‡d. 440 of a farthing. Here I multiply the given decimal by 20, the number of parts of the next less denomination, viz. fhillings, and from the product I separate the three figures on the right hand, 280, as there are Nree places of decimals in the given number. I then multiply these separated figures 280 by 12, and from the product 3360 I feparate the three first figures 360, as before, to be multiplied by the parts of the next denomination, viz. 4; then the figures ftanding on the left hand of these separated figures will be the answer.-115. 3‡d. The same rule ferves to discover the value of any other integers, having regard to the number of parts contained in each inferior denomination. Thus to find the value of a decimal fraction of a pound troy, I first multiply the fraction by 12 to find the ounces, then the separated figures by 20 to find the pennyweights, and lastly by 24 to discover the grains. Qu. 24. 2. What is the value of .6725 of a cwt.?-Anfwer 2qrs. 19lb. 5oz. Qu. 3. What is the value of .61 of a ton of wine?— Anf. 2hhds. 27galls. 2qts. pt. Cafe 3. To find the value of a decimal of a pound sterling, by inspection. Rule. Double the first figure of the decimal on the left hand for fhillings; and if the next figure be 5, or above 5, add 1 fhilling more to it: then call the figures in the second and third places farthings (after deducting 5 from the fecond figure if necessary), and if the number of farthings be above 12 abate one, and if above 37 abate 2. The other figures in the fraction, if more, are neglected. Example Example 1. Find the value of .564 of a pound by inspec tion. IOS. For the 5 take 31 II 34 Here I take the double of 5, the first figure, for fhillings, which is so, alfo fhilling inore for the 5' contained in the 6, and the remaining 14 (viz. 1 in the 6, and 4) I confider as farthings, abating 1 because they are above 12, which make 3d. thus the decimal .564 of a pound is 115. 34d. as may be seen in Case 4. Qu. 2. Find the value of .7880 of a pound by infpection, -Aufwer 15s. 9d. Qu. 3. Find the value of .14729 of a pound by inspection, -Anf. 25. 114d. Cafe 4. To find the decimal fraction of a pound equal to any given number of fhillings and pence. Rule. Write half the greatest even number of fhillings for the first figure in the decimal, and the number of farthings in the pence and farthings for the fecond and third figures, obferving to add 5 more to the fecond figure, if the number of fillings be odd; alfo add one more to the third figure, if the farthings exceed 12, and add 2 if they exceed 37. Example 1. Find the decimal fraction of a pound equal to 115. 3&d. For half 10 take .014 .564 Here for the 11s. I take of the next greatest even number, which is 5, for the first figure of the decimal, and for the odd fhilling, place 5 to be added to the second figure; then for the 34d. I take 14 to be added to the second and third numbers, as there are 13 farthings in 34d. and 1 is added, as the farthings are above 12; thus, the decimal is .564 of a pound. Qu. 2. Find the decimal equal to 18s. 44d.-Anf. .919. Qu. 3. Find the decimal equal to 175. 61d.—Ans. .878. VOL. I. LI SECT. 1 SECT. II. OF ADDITION OF DECIMALS. ADDITION of decimal fractions is performed in the fams manner as addition of whole numbers, except in the diípofition of the figures. Rule. Place the figures exactly under each other, according to the value of their places, that is, the whole numbers (if any) under each other, as in addition of whole numbers, and the fractions are alfo to be placed according to their values, viz. primes under primes, feconds under seconds, &c. Then find their fum as in whole numbers, and point off as many places for decimals as are equal to the greatest number of decimal places in any of the given numbers. Example 1. What is the fum of 22.5709, 1.03, 1492.001, 2.971, .00726? 22.5709 1.03 1492.001 2.971 .00726 Here the numbers are added together like whole numbers, and the number of places pointed off for decimals are 5, equal to the greatest number of decimal places in any of the given numbers. The figures on the left hand of the decimal point are whole numbers or integers. More Examples. 1518.58016 SECT. III. OF SUBTRACTION OF DECIMALS. DECIMAL fractions are fubtracted in the fame manner as whole numbers, but the numbers are placed and the decimals pointed off according to the rule given in the foregoing fection. Example 1. What is the difference of 247.0729 and 3746.805732? Here the uppermost number confifts of 6 places of decimals, wherefore the remainder fought must have as many decimal places; in 3746.805732 247.0729 3499-732832 every other respect it is wrought like fubtraction of whole RULE. Multiply the given numbers one by the other, as in whole numbers. Then point off as many figures for decimals as there are decimal places in both the numbers; but if there be not fo many places in the product, as many cyphers must be prefixed on the left hand thereof as will make up the number of decimal places required. Example 1. Multiply 2 03271 by .0056. |