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From 71.45 take 8.4837248.

Difference=62.9662752.
From 84 take 82.3412.

Diff.=1.6588.

MULTIPLICATION OF DECIMALS. Set the multiplier under the multiplicand without any regard to the situation of the decimal point; and having multiplied as in whole numbers, cut off as many places for decimals in the product, counting from the right hand towards the left, as there are in both the multiplicand and multiplier : but if there be not a sufficient number of places in the product, the defect may be supplied by prefixing ciphers thereto.

For the denominator of the product being an unit, prefixed to as many ciphers, as the denominators of the multiplier and multiplicand contain of ciphers, it follows, that the places of decimals in the product, will be as many as in the numbers from whence it arose.

EXAMPLES.

Multiply 48.765 by .003609

,003609

438885 292590

146995 Product=.175992885 Multiply

.121
by .14

484
121

Product=.01694

Multiply 121.6 by 2.76

2.76

7296 8512 2432

Product=335.616

Multiply .0089789 by 1085

Product=9.7421065

Multiply .248723 by .13587

Product=.03379399401.

DIVISION OF DECIMALS. Divide as in whole numbers ; observing that the divisor and quotient together must contain as many decimal places as there are in the dividend. If, therefore, the dividend have just as many places of decimals as the divisor has, the quotient will be a whole number without any decimal figures. If there be more places of decimals in the dividend, than there are in the divisor, point off as many figures in the quotient for decimals, as the decimal places in the dividend exceed those in the divisor ; the want of places in the quotient being supplied by prefixing ciphers. But if there be more decimal places in the divisor, than in the dividend. annex ciphers to the dividend, so that the decimal places here may be equal, in number, to those in the divisor; and then the quotient will be a whole number, without fractions.

When there is a remainder, after the division has been thus performed, annex ciphers to this remainder, and continue the operation till nothing remains, or till a sufficient number of decimals shall be found in the quotient,

EXAMPLES.

Divide .144 by .12

.12).144(1.2=quotient.

12

24 24

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0 Divide 63.72413456922 by 2718 2718)63.724134569220.02344522979=quotient.

5436

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There being 11 decimal figures in the dividend, and none in the divisor, Il figures are to be cut off in the quotient; but as the quotient itself consists of but 10 figures, prefix to them a cipher to complete that number. Divide 1.728 by .012 .012)1.728(144=quotient.

12

52
48

48
48

0 Because the number of decimal figures in the divisor and dividend, are alike, the quotient will be integers.

Divide 2 by 3.1416
3.1416)2.0000,0(0.636618+quotient.

1 8849 6

115040
94248

207920
188496

194240
188496

57440 31416

260240
251228

'G

In this example there are four decimal figures in the divisor, and none in the dividend; therefore, according to the rule, four ciphers are annexed to the dividend, which in this condition, is yet less than the divisor. A cipher must then be put in the quotient, in the place of integers, and other ciphers annexed to the dividend ; and the division being now performed, the decimal figures of the quotient are obtained.

Divide 7234.5 by 6.5 Quotient=1113.
Divide 476.520 by .423 =1126.5+
Divide .45695 by 12.5

-=.0365+ Divide 2.3 by 96

=.02395+ Divide 87446071 by .004387- =19933000000. Divide .624672 by 482

= .001296.

REDUCTION OF DECIMALS.

RULE I.

To reduce a Vulgar Fraction to a Decimal of the

same value.

I Laving annexed a sufficient number of ciphers, as decimals, to the numerator of the vulgar fraction, divide by the denominator ; and the quotient thence arising, will be the decimal fraction required.

EXAMPLES.

Reduce to a decimal fraction.

4)3.00

.75 =decimal required. For å of one acre, mile, yard, or any thing, is equal to 1 of 3 acres, miles, yards, &c. there

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