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Place the number, as in addition, with the least under the greatest; and in the difference, set the point directly under those in the example.
EXAMPLES, Yards. Gallons. Miles.
Acres. 576.271 3618.218
6827.4681 89.7167 1981,85
| From 100.17, take 84.476, what is left ?
answer 15.694 2 What is the difference between the sum of 841.46+ 109.62+34.691, and of 478.462x37.66+378.8 ?
MULTIPLICATION OF DECIMALS."
Multiply as in integers, and point off as many decimal places in the product as are in both factors. Note 1. If the decimal places be wanting in the product, sapply them with
ciphers to the decimal point.
2. Multiplication in decimals may le contracted thus; Set the units figure of the multiplier under such place of the multiplicand as is to be the lowest retained in the product; and place all the remaining figures of the multiplier in an inverted order: in multiplying, begin with the figure in the multiplicand which stands over the multiplying figure, adding the increase which may arise, by carrying one for the first five, and one more for every ten after, and place the products so, that the right hand figures stand under each other.
EXAMPLES 1 Multiply 743,56815 by 52,647
Contracted and to retain
Three decimal places. : 745,56 815
743,56 815 52,647
2 Multiply 79,347 by 23,15 facit 1836,88305 3 Multiply ,63478 by ,8264 1524582192 4 Multiply 3,141592 by 52,7438 165,6995001296 5 Multiply ,385746 by ,00463 . ,00178600398 6 Multiply ,002534 by ,03256 ,00008250704
7 Multiply 245,378263 by. 72,4385, reserving 4 places of decimals in the product.
facit 17774,8333 8 Multiply 674,4375 by 27,368, reserving only the integers in the product.
facit 18458 9 Multiply 27,14986 by 92,41035, and retain 6 places of decimals in the product.
facit 2508,928065. 10 Multiply 184,8207 by 18,57493, and retain 3 places of decimals in the product.
When the dividend has not as many decimal places as the divisor, or will not contain it, annex ciphers to supply the defect; then divide as in integers, and point off in the quotient, as many decimal places as the decimal places of the dividend exceed those in the divisor, Or,
Let the divisor be conceived to stand under the containing left hand figures of the dividend, and the first figure of the quotient will possess the same place of integers or decimals, as that in the dividend which corresponds to the units place of the divisor.
When there are many figures in the divisor the operation may be contracted, thus;
Find what place of integers, or decimals, the first figure of the quotient will possess; and consider how many quotient figures will serve the present purpose; then take the same number of the left hand of the divisor, and as many of the dividend as will contain them (less than ten times) rejecting the rest; then, instead of bringing figures down from the dividend, separate one from the right of the divisor, as often as necessary, till the whole be exhausted ; remembering to carry from the right hand figures of the divisor as in contracted multiplication. ling : When there are not so many figures in the divisor, di
vide as usual, till there be as many of the quotient figures found as the divisor is short of the intended quotient; then use the contraction.
Contracted so as to have three decimal places in the quotient :: 92,4103,5)2508,92806(27,149+facit. ...
: :: .80 2 Divide 1836,88305 by 23,15
facit 79,347 3 Divide 3673,7661 by 158,674
25,15 4 Divide 234,70525 by 64,25 "
3,653 5 Divide 9,
by ,9 6 Divide ,9
by 9, hy Divide 3
by 3, & Divide ,00178600398 by ,00463 . ,385746
9 Divide 2508,928065051 by 92,41035, so as to have 4 places of decimals in the quotient.
facit 27,1498 10 Divide ,00357200796 by ,771492 f acit ,00463
11 Divide 87,076326 by 9,365407, and let there be 7 places of decimals in the quotient.
facit 9,2976552 12 Divide 174,152652 by 18,730814, and let there be 3 places of decimals in the quotient.
REDUCTION OF DECIMALS.
CASE 1. -
; RULE. Annex as many ciphers to the numerator as may be necessary, which divide by the denominator.
Note. The quotient must consist of as many decimal pla
ces, as there are ciphers annexed. If a compound fraction be given, reduce it first to a single one.
EXAMPLES. 1 Reduce to a decimal.
facit ,25 2 Reduce 1 to a decimal. . facit ,5 3 Reduce to a decimal.
,75 4 Reduce to a decimal.
,1923+ 5 Reduce 24 to a decimal.
,45614+ 6 Reduce 1 of 1 to a decimal.
1,6043956+ 7 Reduce ii of of to a decimal. ,07766+ 8 What is the equivalent decimal for ? answer ,375 9 What is the decimal of 1?
,04 10 What are the equivalent decimals for 16, 7, 6, 7 and
"answer 955, ,95, 9375, 875, 0546875
a CASE 2. To reduce any sum, or quantity, to the decimal of a given denomination ;
First. Divide the given sum, &c. in its lowest mentioned denomination, by the number of like parts in the proposed integer; the quotient will be the decimal required. Or,
Secondly. Write the given numbers orderly from the least to the greatest in a perpendicular column, and divide each of them by such a number as will reduce it to the next name, annexing the quotient to the succeeding number; the last quotient will be the required deciinal.