Example 1. Find the value of .564 of a pound by inspec tion. For the 5 take IOS. For the 5 in the 6 take 1 II 3 3 Here I take the double of 5, the first figure, for fhillings, which is o, alfo 1 fhilling more for the contained in 5 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 34d.: thus the decimal .564 of a pound is 115. 3ēd. as may be seen in Case 4. Qu. 2. Find the value of .7880 of a pound by inspection, -Aufwer 15s. 9d. Qu. 3. Find the value of .14729 of a pound by inspection, -Anf. 2s. 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 firft 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 fhillings 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 11s. 3 d. For half 10 take .5 .014 .564 Here for the 1 Is. I take of the next greatest even number, which is 5, for the firft figure of the decimal, and for the odd fhilling, place 5 to be added to the fecond figure; then for the 34d. I take 14 to be added to the second and third numbers, as there are 13 farthings in 3 d. and I 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. 63d.—Anf. .878. VOL. I. LI SECT. SECT. II. OF ADDITION OF DECIMALS. ADDITION of decimal fractions is performed in the fame manner as addition of whole numbers, except in the difpofition 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 feconds, &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 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. .00726 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? 247.0729 Here the uppermoft number confifts of 6 3746.805732 places of decimals, wherefore the remainder sought must have as many decimal places; in 3499-732832 every other respect it is wrought like fubtraction of whole numbers. 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. In this example the number of decimal places in both the multiplier and multiplicand is 9; but the product confifts of only 8 figures, therefore I must prefix one cypher on the left hand thereof, which makes the true product. 27.02943 540 58860 810882 900 10811772 116.23195 48860 Examples. 2.03271 .0056 1219626 1016355 011383176 2.20434 .43970 Thus it appears that in multiplication of decimal fractions there is no neceffity for placing thofe figures of the fame value under each other, as in the two foregoing rules *. SECT. V. OF DIVISION OF DECIMALS. THIS rule is alfo performed as divifion of whole numbers, but from the quotient point, off as many figures for decimals as the decimal places in the dividend exceed those in the divifor. But if the places in the quotient be not fo many as fhould be pointed off for decimals, as many cyphers must be placed on the left hand as neceffary. * There is a contracted method of working both this and the following rule given by many writers on arithmetic. They are, however, not very fimple, and may very well be fuperfeded, by omitting fome of the decimals in both numbers, and working according to theg general rule. If at any time there be a remainder, and if it be required to have an answer to a greater degree of exactnefs, as many cyphers may be affixed to the right hand of the dividend as is thought proper. Example 1. Divide 1836.88305 by 23. 15. 23.15)1836.88305(79-347 1620.5 In the fecond example there are 4 decimal places in the dividend, and none in the divifor, therefore there must be 4 places of decimals in the quotient. And in the third example as the number of decimal places in the divifor and dividend are equal, being 4 in each, there must be no decimals in the quotient. Every other rule in arithmetic may be performed by decimal fractions as well as by whole numbers, as the fame rule ferves for both; thus in the rule of three direct in decimals, the fecond and third numbers are multiplied together for a dividend, and the first number is the divifor as in whole Gumbers; and the like may be observed of every other rule. CHAP. |