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SCALE OF NOTATION.
oo tenth parts.
ADDITION OF DECIMALS. Write the numbers under each other according to the value or denomination of their places ; which position will bring all the Decimal points into a column, or vertical line, by themselves. Then, beginning at the right hand column of figures, add in the game manner as in whole numbers, and put the decimal point, in the sum directly beneath the other points.
Add 4.7832 3.2543 7.8251 6.03 2.857 and 3.251 together. Place them thus,
4.7832 3,2543 17.8251 6.03 2.857 3.251
Add 6.2 121.306 .75 2.7 and .0007 to. gether. 121.306
.75 2.7 .0007
Sum = 130.9567
What is the sum of 6.57 1.026 .75 146.5 8.1 526. 3.97 and .0271 ?
What is the sum of 4.51 146.071 .507 .0006 132. 62.71 .507 7.9 and .10712!
SUBTRACTION OF DECIMALS. Write the figures of the subtrahend beneath those of the minuend according to the denomination of their places, as directed in the rule of addition; then, beginning at the right hand subtract as in whole numbers, and place the decimal point in the difference exactly under the other two points.
From 71.45 take 8.4837248.
Difference = 62.9662752.
MULTIPLICATION OF DECIMALS.
Set the multiplier under the multiplicand without any regard to the situation of the decimal point; and having multiplied as in whole numbers, cut off as many places for decimals in the product, counting from the right hand towards the left, as there are in both the multiplicand and multiplier: but if there be not a suflicient number of places in the product, the defect may be supplied by prefixing ciphers thereto.
For the denominator of the product being an unit, prefixed to as many ciphers, as the denominators of the multiplier and multiplicand contain of ciphers, it follows, that the places of decimals in the product will be as many as in the numbers from whence it arose.
Multiply 48.765 by .003609
146295 Product =.175992885
121 Product = .01694
Multiply 121.6 by 2.76
7296 8512 2432
Product = 335.616
Multiply .0089789 by 1085
Product = 9.7421065
Product = .03379399401. DIVISION OF DECIMALS. Divide as in whole numbers; observing that the divisor and quotient together must contain as many decimal places as there are in the dividend, if, therefore, the dividend have just as many places of decimals as the divisor has, the quotient will be a whole number without any decimal figures. If there be more places of decimals in the dividend, than there are in the divisor, point off as many figures in the quotient for decimals, as the decimal places in the dividend exceed those in the divisor; the want of places in the quotient being supplied by prefixing ciphers. But if there be more decimal places in the divisor, than in the dividend, annex ciphers to the dividend, so that the decimal places here may be equal, in number, to those in the divisor; and then the quotient will be a whole number, without fractions.
When there is a remainder, after the division bas been thus performed, annex ciphers to this remainder, and continue the operation till nothing remains, or till a sufficient number of decimals shall be found in the quotient.