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SUBTRACTION OF DECIMALS.
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.
rards. 576.270 89.7167
Gallons. 3618.218 1981.85
Miles. 246111 9716.701
Acres. 6827.4681 6018.91
answer 15.694 2 What is the difference between the sum of 841.46+ 109.62 +34 691, and of 478.462 +37.66+ 378.8 ?
MULTIPLICATION OF DECIMALS
Multiply as in integers, and point off as many decimal places in the product, as are in both the factors. Note I. If the decimal places be waiting in the product, supply them
with ciphers to the decimal point,
2. Multiplication in decimals may be contracted thus ; Set the units figure of the multiplier under such place of the multipia cand, 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 multip'icand 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 for that the right hand figures stand under each other.
2 Multiply 79,347 by 29,15 facit 1836,88305 3 Multiply ,63478 by ,8264 ,524582192 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 places of decimals in the product.
facit. 17774,8333 8 Multiply 674,4375 by 27.368, reserving only the integers in the product.
9 Multiply 27,14986 by 92.41035, and retain 6 places of decimals in the product
facit 2508,928065 10 Multiply 184,8207 by 13,57493, and retain 3 places of decimals in the product.
When the dividend has not as many decimal places a: 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.
When there are not so many figures in the divisor, divide 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.
by ,9 by.9
2 Divide 1836,88305
by 23,15 facit 79,347
>385746 9 Divide 2508,928065051 by 92,41035, so as to have 4 places of decimals in the quotient.
facit 27,1498 10 Divide ,00357300796 by ,771492 facit ,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.
To reduce a vulgar fraction to a decimal ;
RULE. Annex as many ciphers to the numerator as may be néces. sary, which divide by the denominator.,
Note. The quotient must conlist of as many decimal places, as there are
ciphers annexed. a compound fraction be given, reduce it first to a single one.
1. Reduced to a decimal.
4)1.00 facit .25
2 Reduce } to a decimal.
facit 5 3 Reduce to a decimal.
275 4 Reduce ' to a decimal.
,1923+ 5 Reduce to a decimal.
245614+ 6 Reduce 11 of 1; to a decimal.
,6043956+ 7 Reduce tof of i'r to a decimal, ,07766+ 8 What is the equivalent decimal for
answer ,375 9 What is the decimal of 15?
,04 1o What are the equivalent decimals for the food and and ?
answer 155, 195, 1375, ,875, 90546875
CASE 2. To reduce any sum, or quantity, to the decimal of a given denomination;
Trirst, 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 decimal.