Ciphers placed at the right hand of a decimal fraction do not alter its value, since every significant figure continues to possess the same place: so,5,50 and ,500 are all the same value, and equal to or But ciphers placed at the left hand of decimals, decrease their value in a tenfold proportion, by removing them further from the decimal point. Thus, ,5,05,005, &c. are five tenth parts, five hundredth parts, five thou sandth parts, &c. respectively. It is therefore evident that the magnitude of a decimal fraction, compared with another, does not depend upon the number of its figures, but upon the value of its first left hand figure: for instance, a fraction beginning with any figure less than ,9 such as ,899229, &c. if extended to an infinite number of figures, will not equal,9. ADDITION OF DECIMALS. RULE. 1. Place the numbers whether mixed or pure decimals, under each other, according to the value of their places. 2. Find their sum as in whole numbers, and point off so many places for the decimals, as are equal to the greatest number of decimal parts in any of the given numbers. EXAMPLES. 1. Find the sum of 41,653 +36,05+24,009+1,6 Thus, 41,653 24,009 1,6 312 1 Sum, 103,312 which is 103 integers, and parts of unit. Or, it is 103 units, and 3 tenth parts, 1 hundredth part, and 2 thousandth parts of a unit, or 1. a Hen we may observe, that decimais, and FEDERAL MEY, are subject to one, and the same law of notation, and consequently of operation. For since dollar is the money unit; and a dime being the tenth, a cent the hundreth, and a mill the thousandth part of a dollar, or unit, it is evident that any number of dollars, dimes, cents and mills, is simply the expression of dollars, and decimal parts of a dollar: Thus, 11 dollars, 6 dimes, 5 cents, = 11,65 or 11,65 dol. &c. 100 5. Add the following sums of Dollars together, viz. $12,34565+7,891+2,34+14,+,0011 Ans. $36,57775, or $36, 5di. 7cts. 775mills. 6. Add the following parts of an acre together, viz. ,7569+,25+,654,199 Ans. 1,8599 acres. 7. Add 72,5+32,071+2,1574+371,4+2,75 8. Add 30,07+200,71+59,4+3207,1 Ans. 480,8784 Ans. 3497,28 9. Add 71,467+27,94+16,084+98,009+86,5 10. Add ,7509+,0074+,69+,8408+,6109 11. Add ,6+,099+,37+,905+,026 Ans. 300 Ans. 2,9 Ans. 2 12. To 9,999999 add one millionth part of a unit, and the sum will be 10. 13. Find the sum of Twenty-five hundredths, Three hundred and sixty-five thousandths, Six tenths, and nine millionths Answer, 1,215009. SUBTRACTION OF DECIMALS. RULE. Place the numbers according to their value; then subtract as in whole numbers, and point off the decimals as in Addition. 12. From 107 take,0007 Ans. 234,9925 Ans. $235,451 Ans. 55,3 Ans. 194,7925 Ans. 106,9993 13. From a unit, or 1, subtract the millionth part of itself. Ans. ,999999 444 MULTIPLICATION OF DECIMALS RULE. 1. Whether they be mixed numbers, or pure decimals, place the factors and multiply them as in whole numbers. 2. Point off so many figures from the product as there are decimal places in both the factors; and if there be not so many places in the product, supply the defect by prefixing ciphers to the left hand. 8. What cost 6,21 yards of cloth, at 2 dols. 32 cents, 5 mills per yard? Ans. $14, 4d. 3c. 8m. 9. Multiply 7,02 dollars by 5,27 dollars. Ans: 36,9954dols. or $36 99cts. 5m. 10. Multiply 41 dols. 25 cts. by 120 dollars. 11. Multiply 3 dols. 45 cts. by 16 cts. Ans. $4950 Ans. $0,5520=55cts. 2mills. 12. Multiply 65 cents, by ,09 or 9 cents. Ans. $0,0585=5cts. 8mills. 13. Multiply 10 dols. by 10 cts. Ans. $1 Ans. $2,39+ To multiply by 10, 100, 1000, &c. remove the separating point so many places to the right hand, as the multiplier has ciphers. Multiplied by 10, niakes 4,25 So,425 by 100, makes 42,5 by 1000, is ,425 For ,425x10 is 4,250, &c. DIVISION OF DECIMALS. RULE. 1. The places of the decimal parts of 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 places for decimals, as the decimal places in the dividend exceed those in the divisor. 2. If the places in the quotient be not so many as the rule requires, supply the defect by prefixing ciphers to the left hand of said quotient. NOTE. If the decimal places in the divisor be more than those in the dividend, annex as many ciphers to the dividend as you please, so as to make it equal, (at least) to the divisor. Or, if there be a remainder, you may annex ciphers to it, and carry on the quotient to any de gree of exactness. 13. If 212 or 21,75 yards of cloth cost 34,317 dollars, what will one yard cost? $1,577+ NOTE. When decimals, or whole numbers, are to be divided by 10, 100, 1000, &c. (viz. unity with ciphers, |