Example. ]educe .44005 of a foot to a decimal.
,44005 12 5.28060 l 3.3672 4.4064 12 4.8768 To add decimals ; write down the several parts under their respective denominators, viz., all the points in a vertical line, the tenths in a succeeding vertical line, and so on ; add the several columns, as in co/ninon addition, from right to left ; place a point under the column of points, or cut off as many decimal parts from the right-hand figure towards the left, as there arc columns, and the figure or figures upon the left-hand side of the point, if any, will be integers, and those upon the right-hand side of the point will be decimals.
Example I. Add the following decimals together, viz., .7854, .07958, .5236.
.7354 .0795S .5236 1.38353 the sum required.
To subtract decimals ; place the numbers as in addition, the less under the greater, and perform the operation as in subtraction of integers.
Example I. Subtract .25 from .75.
.75 .25 .50 the nuwber required.
If the parts of a foot are given in feet, inches, &c., they must be reduced to the farthest denomination from the place of feet.
To multiply in decimals, proceed as in multiplication of integers, and point as many figures, begiiming with the first figure from the right in the product, as the number of decimak in both fitetors ; and the remaining figures, if any. upon the left-hand, will be integers ; but if there are not as many figures in the product as in both, the delieieney must be made up by the addition of one or more ciphers.
Example I.
Multiply .9087 by .852 18174 45435 72696 Product .7742124 in large decimals, the work may be contracted thus • Write the units' place of the multiplier under that place of the decimals in the multiplicand, whose place you would reserve in the product ; write the other figures in the multi. plier in a contrary order.
Begin with the figure of the multiplier nearest the right band, and multiply by the next figure towards the right of it, in the multiplicand, if' any ; and if this product be five, or above five, in the number of tens in the prodnet, carry one more than there are tens in the last product to the next product ; then set down the overplus above the tens for the first figure, and carry the tens to the neat place. and procee
through the line as in common multiplication. Proceed with every other line in the same manner, observing, however to place the first figure of every line directly under the first figure of the last line, and the product so found will be thy answer.
Example I.—What is the product of .9057 multiplied by .852, in order to retain four places of decimals? By contraction. By the common method.
.90S7 .9037 258.0 .852 7270 = 908 x 6 18172 454 = 90 X 5 + 4 45435 18 = 9 x 2 + 0 72696 .7742 .7742122 In this example, the multiplier being placed as directed, begin with 8, the first figure of the multiplier, and multiply it by 7, the next figure to the right of it in the multiplicand, and the product is 56, which is more than 5 above 5 tens, therefore carry 6: multiply S by the next figure, 8 towards the left, the product is 04, and 6 carried, makes 70, set down a cipher for the first figure, and carry 7 to the next ; proceed thus for the whole line, and 7:270 will be the product. Pro ceed with the remaining figures of the multiplier, in the same manner, writing down the left-hand figures of every row under each other.
To divide a decimal or mixed number by a decimal or mixed number : divide as in whole numbers, and cut off as mane figures from the right-hand of the quotient as the deci mal places of the dividend exceed those of the divisor.
If the number of figures in the quotient be less than the of the decimal figures in the dividend above those of the divisor, the defect must be supplied by prefixing ciphers on the left hand. Should there be a remainder, annex ciphers to it, and thus the quotient may he carried to any degree of exactness, observing, however, that every cipher annexed in carry ing out the work, must be accounted a decimal place in the dividend.
Example 1,—Divide 43.95 by 5.
.5)43.95 S.79 the quotient required. Example IL—Divide 4.308 by .0078.
.0078)4.3680 (560 390 468 46S ...0