9. Reduce 54 gallons to the fraction of a hogshead of wine. Ans. to. What part of a hogshead is 9 gallons ? 11. What part of a pound troy is 10oz. 10pwt. 10grs. ? Ans. 1 Ans. Ma 45 DECIMAL FRACTIONS. A Decimal Fraction is that whose denominator is an unit, with a cypher, or cyphers annexed to it, Thus, io, Todi Tomo, &c. &c. The integer is always divided either into 10, 100, 1000, &c. equal parts; consequently the denominator of the fraction will always, be either 10, 100, 1000, or 10000, &c. which being understood, need not be expressed; for the true value of the fraction may be expressed by writing the numerator only with a point before it on the left hand thus, fo, is written ,5; 16,45; 1986,725, &c. But if the numerator has not so many places as the denominator has cyphers, put so many cyphers before it, viz. at the left hand, as will make up the defect; so rite sio thus, ,05; and 1067 thus, ,006, &c. NOTE. The point prefixed is called the separatrix. Decimals are counted from the left towards the right hand, and each figure takes its value by its distance from the unit's place ; if it be in the first place after units, (or separating point) it signifies tenths; if in the second, hundredths, &c. decreasing in each place in a tenfold proportion, as in the following NUMERATION TABLE. Millions. C. Thousands, Tens. Tenth parts. Thousandth parts. Whole Numbers. a Cyphers 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 et revalue, and equal to so or . Laers placed at the left hand of decimals, decrease 1 eir value in a tenfolel proportion, by removing them igrtner from the decimal point. Thus, 95,05 ,005, &c. are tive tenth parts, five hundredth parts, five thousanat 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 ,899209, &c. if extended to an infinite number of figures, will not equal ,9. ADDITION ON DECIMALS. RULE. 1. Place the numbers, whether mixed or pure decimal under each other, according to the value of their places 2. Find their sum as in whole numbers, and point of 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 suni of 41,653-_-36,05-4-24,009-+1,6. 741,653 56,05 Thus, 24,009 Sum, 103,512 which is 103 integers, and your parts of an unit. Or, it is 103 units, and 3 tenth parts, 1 hundredth part, and 2 thousandth parts of an unit, or 1. Hence we may observe, that Decimals, and FEDERAL MONEY, are subject to one, and the same law of notations Ara conseguentiy of operation. a a For since dollar is the money unit; and a dime being the tenth, a cent the hundredth, and a mill the thousandth a 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 117 dol. &c. 2. Add the following mixed numbers together. (2) (3) (4) Dollars. 48,9103 1,8191 3,1050 ,7012 5. Add the following sums of Dollars together, viz. $12,34565+7,391+2,54+14,+,0011 Ans. $56,57775, or $56, 5di. 7cts. 716 mills. 6. Add the following parts of an acre together, viz. ,7569+,25+,654-1,199 Ans. 1,8599. acres. 7. Add 72,5-+-32,071+2,15744-571,4+2,75 Ans. 480,8784 8. Add 30,07 ---200,71 +59,4+3207,1 Ans. S497,28 9. Add 71,467 +27,94+16,0844-98,0094-86,5 Ans. SOO 10. Add ,7509+,0074+,69+,8408+-,6109 Ans. 2,9 11. Add ,6+,099+,57 +,905+,026 Ans. 2 12. To 9,999999 add one millionth part of an unite and the sum will be 10. 13. Find the sum of Ansil'er, 1,215009 SUBTRACTION OF DECIMALS. EXAMPLES. RULE. Place the numbers according to their value; then subtract as in whole numbers, and point off' the decimals as in Addition. 6, From 480 take 215,0075 Ans. 254,9925 7. From 256 dols. take ,549 dols. Ans. $235,451 8. From ,145 take ,09684 Ans. ,04816 9. From ,0754 take ,2571 Ans. ,0383 10. From 271 take 215,7 Ans. 55,3 11. From 270,2 take 75,1075 Ans. 194,7925 12. Fron 107 take ,0007 ns. 106,9993 13. From an unit, or 1, subtract the millionth part of itself. 2ns. ,999999 1. Whether they be mixed numbers, or pure decimals, place the factors and multiply them as in whole nunibers. 2. Point of so many tigures 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 select by prefixing cyphers to the left hand. 1. Multiply 5,236 by ,008 2. Multiply 3,024 by 2,23 Product ,041888 6,74352 25 3. Multiply 25,238 by 12,17 sistens, 307,14646 4. Multiply 2461 by 9329 130,1869 5. Multiply 7853 by 5,5 27485,5 6. Multiply ,007853 by ,035 ,000274855 7. Multiply ,004 by ,004 ,000016 8. What cost 6,21 yards of cloth, at 2 dols. 32 cents, 5 mills, per yard ? Ans. $14, 4d. Sc. 8. 12. 9. Multiply 7,02 dollars, by 5,27 dollars. Ans. 36,9954dols. or $36 99cts. 57m. 10. Multiply 41 dols. 25 cts. by 120 dollars. Ans. $4950 11. Multiply 3 dols. 45 cts. by 16 cts. Ans. $0,5520=55cts, 2mills. 12. Multiply 65 cents, by ,09 or 9 cents. Ans. $0,0585=5cts. 83mills. 13. Multiply 10 dols. by 10 cts. Ans. 21 14. Multiply 341,45 doss. by ,007 or 7 mills. Ans. 82,59+ To multiply by 10, 100, 1000, &c. remove the separa. ting point so many places to the right hand, as the multiplier has cyphers. Multiplied by 10, makes 4,25 by 100, makes 42,5 is For ,425 X 10 is 4,250, &c. 425, 1. The places of the decimal parts of the divisor and @yotient cuantcıl towether, must always bc cqual to those |