MULTIPLICATION OF DECIMALS.

RULE. Multiply exactly as in whole numbers, and from the right of the product point off as many places for decimals, as are equal to the decimal places in the multiplicand and multiplier, counted together; If at any time there, are not so many places in the product, as this rule requires, supply the defect by prefixing cyphers.

N. B. In the 1st example there are three decimal figures in the multiplicand and multiplier, therefore three figures in the product are pointed off for decimals.

In the 2d example there is only one figure in decimals, in the multiplier and multiplicand: therefore one figure in the product is pointed off for decimals.

In the 4th example there are six figures in decimals, in the multiplier and multiplicand; and there are only 5 figures in the product; therefore one cypher is prefixed, and all are pointed off for decimals, &c.

N. B. The multiplication of decimals is the multiplication of American money, &c.

Examples.

1. How much is the product of 29.5 multiplied by 96 Ans. $28.32 cents.

cents?

2. How much will 1000 pounds of butter come to, at 114 cents per pound?

Ans. 115.

DIVISION OF DECIMALS.

RULE. Divide exactly as in whole numbers, and from the right hand of the product point off as many places for decimals, as the decimal places in the dividend exceed the decimal places in the divisor; If there are not so many places in the quotient as this rule requires, the defect must be supplied by prefixing cyphers to the left of the quotient; if there are more decimal places in the divisor than in the dividend, place as many cyphers to the right of the dividend, as will make them equal, and the quotient is whole numbers till the dividend is all brought down: If a remainder still remains annex cyphers and continue the division; and the quotient thence arising will be decimals.

Examples.

1. Divide 34-21 by 12.1.

12.1)34·21(2·827

242

1001

968

330

242

880

847

33 Remainder.

NOTE 1. In this first example there is one more decimal in the dividend, than in the divisor: I therefore pointed off one for decimals, and then annexed two cyphers, and continued the division.

2. Divide 1302 by 101.

•101)1 302.000(12891 089 Ans.

NOTE 2. In this example the dividend is whole numbers, and the divisor has 3 places in decimals; I therefore placed 3 cyphers to the right of the dividend before I divided, and after the dividend was all brought down, I annexed 3 cyphers to the remainder, and continued the division, &c.

3. Divide 263.146 by 1320.

1320)263-146( 199,466. Ans.

1320

NOTE 3. In this example there are 3 decimal places in the dividend, and the divisor is whole numbers; therefore I pointed off 3 figures from the quotient, for decimals.

4. Divide 4567 by 333.

333) 4567(00132. Ans.

NOTE 4. In this example, there are 4 figures in decimals in the dividend, and the divisor is whole numbers: the quotient has but 2 figures: I therefore prefixed 2 cyphers to the left of the quotient, and pointed all off for decimals.

5. Divide 07912 by ·111.

•111)·07912(-71-31. Ans.

NOTE 5. In this example there is 2 more decimal places in the dividend, than in the divisor: I therefore pointed off two places in the quotient for decimals.

6. Divide 00444 by 222.

7. Divide ⚫9023 by •11.

Ans. 00002.

Ans. 8.202.

8. Divide 15.735 by 12.

Ans. 1.311+.*

*This mark (†) signifies that the remainder must be added to make the quotient complete.

REDUCTION OF DECIMALS.

CASE I.

To reduce Vulgar Fractions to Decimals.

RULE. Annex cyphers to the numerator, and divide by the denominator: the quotient is the decimal sought.

Examples.

1. Reduce to a decimal of the same value.

6)5.000

833 Answer.

2. Reduce to a decimal of the same value.

2)1.0

•5 Answer.

3. Reduce to a decimal of the same value.

Ans. 25.

4. Reduce to a decimal of the same value.

Ans. 75.

CASE II.

To reduce different denominations to decimals.

RULE. Write down the several denominations under each other: beginning with the lowest and ending with the highest: on the left of these draw a perpendicular line, and on the left of the line, place such numbers for divisors, against each denomination, as it takes of this to make one of the next higher: annex cyphers to the top figures and divide by the number standing against it on the left of the line: set the quotient (decimally) against the next denomination below; divide the next below by the number standing against it set the quotient as before; proceed thus through all the denominations, the last quotient is the deci mal sought.

Examples.

1. Reduce 198. 11d. 3grs. to the decimal of a pound.

2. Reduce 6 oz. 12 pwt. 15 grs. to the decimal of a pound, Troy weight.

3. Reduce 2 cwt. 3 qrs. 12 lb. 12 oz. 11 dr. to the decimal of a ton, Avoirdupois weight.

4. Reduce 3 qrs. 3. na. to the decimal of a yard, Cloth

measure."

4

9375 Ans.