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

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Multiply .0089789 by 1085

Answer 9.7421065

Multiply .248723 by .13587

Answer .03379399401

DIVISION OF DECIMALS.

Having divided as in whole numbers, annexing cyphers to the dividend if they be wanted; the decimal places in the divisor and quotient must be equal to: those in the dividend, and the defect supplied by prefixing cyphers to the quotient.

For the dividend is a product, contained under the divisor and quotient; and that product contains as many places of decimals as the numbers do from whence it arose; therefore, the difference between the number of decimals in the dividend and divisor, must be cut off in the quotient.

EXAMPLES.

Divide .144 by .12

.12).144(1.2

24

Divide 63.72413456922 by 2718

2718)63.724131569221.02341522979

9364

12101

12293

14214

6245

8096

26609

21472

24462

Answer .02344522979

There being 11 decimal figures in the dividend, and none in the divisor, 11 figures are to be cut off in the quotient; but as the quotient itself consists of but 10 figures, we prefix to them a cypher to complete that number.

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

Divide 2.00000 by 3.1416

3.1416)2.00000(.636618

115040

207920

194240

57440

260240

8912

There being 4 decimal figures in the divisor, and 10 including the cyphers brought down in the dividend, the difference, which is 6 figures, to be cut off in the quotient. Divide 87446071 by .004387.

Answer 199.33.
Divide .624672 by 482.

Answer .001296.
Divide 66.993548 by 27.4.

Answer 2.44502.

3

PROB. I.

To reduce a Vulgar Fraction to a decimal one of the

same Value.

Having annexed a sufficient number of cyphers 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)3.000.75 Answer.

20

For of one shilling, yard, perch, &c. is equal to one fourth of three shillings, yards, perches, &c. therefore if 3 be divided by 4, the quotient will be the answer.

Reduce to a decimal fraction,

5)2.00.4 Answer.

Reduce it to a decimal fraction.

25)12.00(48 Answer.

200

Reduce ito a decimal fraction,

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