Page images
PDF
EPUB

same ten-fold proportion; as in the following Scale or Table of Notation.

[blocks in formation]

SET the numbers under each other according to the value of their places, like as in whole numbers; in which state the decimal separating points will stand all exactly under each other. Then, beginning at the right-hand, add up all the columns of numbers as in integers; and point off as many places. for decimals, as are in the greatest number of decimal places in any of the lines that are added; or place the point directly below all the other points

EXAMPLES.

1. To add together 29-0146, and 3146 5, and 2109, and •62417, and 14-16

29.0146 3146 5 2109.

•62417

14.16

5299 29877 the Sum.

Ex. 2. What is the sum of 276, 39 213, 72014-9, 417, and 5032 ?

3 What is the sum of 7530, 16.201, 3-0142, 957-13, 6-72119 and 03014.

4. What is the sum of 312-09, 3.5711, 71956 71-498, 9739:215, 179, and .0027?

SUBTRACTION

SUBTRACTION OF DECIMALS.

PLACE the numbers under each other according to the value of their places, as in the last Rule. Then, beginning at the right-hand, subtract as in whole numbers, and point off the decimals as in Addition.

EXAMPLES.

1. To find the difference between 91.73 and 2.138.

91.73
2.138

Ans 89-592 the Difference.

2. Find the diff. between 19185 and 2.73.

3. To subtract 4·90142 from 214-81.

4. Find the diff. between 2714 and 916.

Ans 08115.

Ans. 209-90858.
Ans. 27 13 084.

MULTIPLICATION OF DECIMALS.

PLACE the factors, and multiply them together the same as if they were whole numbers.-Then point off in the product just as many places of decimals as there are decimals in both the factors. But if there be not so many figures in the product, then supply the defect by prefixing ciphers.

1000

4332 = 100000

*The Rule will be evident from this example :-Let it be required to multiply 12 by 361; these numbers are equivalent to 361; the product of which is 04332, by the naand ture of Notation, which consists of as many places as there are ciphers, that is, of as many places as there are in both numbers. And in like manner for any other numbers,

EXAMPLES.

[blocks in formation]

To multiply Decimals by 1 with any number of Ciphers, as by 10, or 100, or 1000, &c.

THIS is done by only removing the decimal point so many places farther to the right-hand, as there are ciphers in the multiplier and subjoining ciphers if need be.

EXAMPLES.

1. The product of 51.3 and 1000 is 51300. 2. The product of 2-714 and 100 is

3. The product of 916 and 1000 is

4. The product of 21.31 and 10000 is

CONTRACTION II,

To Contract the Operation, so as to retain only as many Decimals in the Product as may be thought Necessary, when the Product would naturally contain several more Places.

SET the units' place of the multiplier under that figure of the multiplicand whose place is the same as is to be retained for the last in the product; and dispose of the rest of the figures in the inverted or contrary order to what they are usually placed in. Then, in multiplying, reject all the figures that are more to the right-hand than each multiplying figure, and set down the products, so that their right-hand figures

may

may fall in a column straight below each other; but observing to increase the first figure of every line with what would arise from the figures omitted, in this manner, namely 1 from 5 to 14. 2 from 15 to 24, 3 from 25 to 34. &c; and the sum of all the lines will be the product as required, commonly to the nearest unit in the last figure.

EXAMPLES.

1. To multiply 27-14986 by 92 41035, so as to retain only four places of decimals in the product.

Contracted Way.

27.14986

530:4.29

24434874

[blocks in formation]
[merged small][merged small][merged small][ocr errors][merged small][merged small]

542997 2

244 4874

2508 928 650510

2 Multiply 480 14936 by 272416, retaining only four decimals in the product.

3. Multiply 2490 3048 by 573286, retaining only five decimals in the product.

4. Multiply 325-70 428 by 7218393, retaining only three decimals in the product.

DIVISION OF DECIMALS.

DIVIDE as in whole numbers; and point off in the quotient as many places for decimals, as the decimal places in the dividend exceed those in the divisor*.

The reason of this Rule is evident ; for, since the divisor multiplied by the quotient gives the dividend, therefore the number of decimal places in the dividend, is equal to those in the divisor and quotient, taken together, by the nature of Multiplication; and consequently the quotient itself must contain as many as the dividend exceeds the divisor.

Another

Another way to know the place for the decimal point, is this: The first figure of the quotient must be made to occupy the same place, of integers or decimals, as doth that figure of the dividend which stands over the unit's figure of the first product.

When the places of the quotient are not so many as the Rule requires, the defect is to be supplied by prefixing ciphers.

When there happens to be a remainder after the division, or when the decimal places in the divisor are more than those in the dividend; then ciphers may be annexed to the dividend, and the quotient carried on as far as required.

[blocks in formation]

WHEN the divisor is an integer, with any number of ciphers annexed: cut off those ciphers, and remove the decimal point in the dividend as many places farther to the left as there are ciphers cut off, prefixing ciphers if need be; then proceed as before.

*This is no more than dividing both divisor and dividend by the same number, either 10, or 100, or 1000, &c. according to the number of ciphers cut off, which, leaving them in the same proportion, does not affect the quotient. And, in the same way, the decimal point may be moved the same number of places in both the divisor and dividend either to the right or left, whether they have ciphers or not

EXAMPLES.

« PreviousContinue »