Multiplication of Decimals.

THIS Rule is performed exactly the fame as in whole Numbers; only we must observe to cut off as many Places of Decimals in the Product, as there are Decimals in the Multiplicand and Multiplier added together.

But if the Product hath not so many Figures as there should be Places cut off, the Deficiency must be supplied by prefixing a Cypher or Cyphers on the Left Hand, and then cut them off. A few Examples will fufficiently explain this Rule.

Here are four Figures cut off in the Multiplicand, and three in the Multiplier; therefore I cut off Seven in the Product.

The Number of Places cut off in the Multiplicand and Multiplier are two; but as the Product confifts only of one Figure, the Defect is made up by prefixing the Cypher, and then cutting them both off.

To multiply Decimals by 10, 100, 1000, &c. only remove the Point as many Places further towards the Right Hand as there are Cyphers in the Multiplier.

Division of Decimals.

HERE the Operation is the very fame as in whole Numbers; only when the Quotient is found, we must fubtract the Number of Places cut off in the Divisor, out of the Number cut off in the Dividend, and the Remainder shews how many Places must be cut off in the Quotient.

But if the Quotient hath not so many Figures as there should be Decimal Places in it, we must prefix as many Cyphers as will make up the Number of Places, and then cut them off, as in the following Examples.

Here the Decimal Parts in the Dividend exceed those in the Divisor by two; we therefore cut off two Places for Decimals in the Quotient. By this Means we find that the Divifor is contained in the Dividend 20 Times, and 32 hundredth Parts of another.

Example 2.

Divide .6474 by 73.

73).6474 (.0088 the Answer.
584

634

584

(50)

Here the Quotient is 88; but as there are four Places of Decimals in the Dividend, and none in the Divisor, four Places must be cut off in the Quotient. We therefore prefix two Cyphers to the Figures in the Quotient, and it becomes.0088, the Answer, with a small Remainder.

Example 3.

Divide 295.75 b 8.45.

8.45) 295.75 (35

2535

4225 4225

....

Here the Number of Decimal Places in the Dividend and Divifor being equal, the Quotient will be a whole Number; that is, the Divifor is contained in the Dividend just thirty-five Times.

Example 4.

Divide 192.1 by 7.684.

7.684) 192.100 ( 25 the Answer required.

15368

38420

38420

....

Because here are not so many Places of Decimals in the Dividend as they are in the Divisor; we annex Cyphers to the Dividend to make them equal, and the Quotient is in this Cafe a whole Number.

Example 5.

Divide 500l. among 26 Men, and give each Man's Share.

26) 500 (19.231. for Answer.

26

240

234

60.

52

80.

78

(2)

In Questions of this Kind, where a whole Number is divided by a whole Number, we may find the Value of the Remainder to what Exactness we please, by adding a Cypher at a Time to it, remembering, that for every Cypher we add, there must be a Decimal in the Quotient. Here are two Cyphers added, therefore we have two Decimal Places in the Quotient.