In the first example, there being three places of decimals in the multiplicand, and three in the multiplier, I point off six figures in the product; and in the second example, there being five places in the multiplicand, and eight in the multiplier, that is, thirteen in both, I prefix four cyphers to the product, to make the number of places equal to what the rule requires.

3. Multiply 803,27 by 37,076.

Prod. 29782,03852.

4. Multiply 706,321 by ,00245.

5. Multiply ,0732 by 0106.

Prod. 1,73048645.

Prod. ,00077592.

To multiply by 10, 100, 1000, &c. remove the separating point so many figures to the right hand, as the multiplier has cyphers.

RULE.

128,

1. The places of decimal parts in the divisor and quotient counted together, must always be equal to

those in the dividend; therefore, divide as in whole numbers, and from the right hand of the quotient point off so many figures, for decimal parts, as the places in the dividend exceed those in the divisor.

2. But if the places in the quotient be not so many as the rule directs, supply the defect by prefixing cyphers at the left hand.

3. When there are not so many places of decimals in the dividend as in the divisor, supply the defect by annexing cyphers; then the quotient will be whole numbers, and if any thing remain, you may annex cyphers to it, and divide as before.

5. Divide ,0046319 by 182.

Quotient, 00002545.

6. Divide 3278,21 by,12796.

Quotient, 25619,&c.

To divide by 10, 100, 1000, &c. remove the separating point so many places toward the left hand, as there are cyphers in the divisor.

10

3,58.

100 quotient

,358.

,0358.

Thus, 35,8 divided by
{divided by {100}

Reduction of Decimals.

CASE 1.

To reduce a vulgar fraction to its equivalent decimal.

RULE.

Annex cyphers to the numerator, and divide by the denominator; then, as many cyphers as you annexed to the numerator, so many places must be pointed off in the quotient; and if there be not so many places, supply the defect, by prefixing cyphers, according to the rule in division of de cimals.

EXAMPLES.

1. Reduce to a decimal.

8)3,000

Answer, ,375

2. Reduce to a decimal.

16)7,0000(4375 Ans.

64

60

48

120

1.12.

80

80

3. Reduce,,,,, and, to decimals.

Answers,,2.,8.

2222 &c.

4. Reducer,

cimals.

42857&c. ,666 &c. 6. and

289

3

18, 18, and 17 to de-.

Answers, ,0219885. ,99655. ,3144. and ,9966.

CASE 2.

To reduce numbers of different denominations, as of money, weights, and measures, to decimals retaining the same value..

RULE 1. Set down the given numbers perpendic larly, under each other, proceeding orderly from the least to the greatest, for dividends.

2. At the left hand of each number, place such a number for a divisor, as will bring it to the next greater denomination.

3. Beginning with the highest, divide each dividend by its divisor, setting its quotient, as decimal parts, on the right hand of the dividend next below it; and the last quotient will be the decimal sought..