6. How much is it of an hundred weight? Ans. Syrs.- 1b. 101402. 7. Wat is the value of of a mile : Ins. 6fur. 26po. 11N. 8 Ilow much is of an cwt. Ans. Syrs. 3lh. luz. 12: dr. 9. Reduce of an El English to its proper quantity Fus. 2yrs. Stua. 10. flow much is , of a hhdl. of wine: Ans, 54gal. 11. What is the value of is of a day: Jur. 1o. min. 35/sec. PROBLEM III. To reduce any given quantity to the fraction of any greater denomization of the same kind. RI'IE. Reduce the given quantity to the lowest terin inentioned for a numerator; then reduce the integral part to the sanie term, for a denominator ; which will be the frac. tion required. F.XAMPL.ES. 1. Reduce 135. Gl. 24rs. to the fraction of a poun... 20 Integral part 13 6 2 given sain, 12 12 960 Denominator. 650 Num. Ans. 548 2. What part of an hundred, upisht is juis. 1411. Syrs. 111/b.=9&ib. JİNN. = 3. What part of a vard is jyrs. Sna.? 4. What part of a pound sterling is 135. 4.1. Ans: 1 5. Flat part of a civii year is 3 weeks, tavs : 6. What part of a mile is Clur. 26po. sydls. 21.: Jur. po. pil. ji. Mrt. 6 26 21700 Num. a mile =52:0 Denim. Ans. 319 7. Reduce 702. 4pwt. to the fraction of a pound try; Ans. 9. Reduce 54 gallons to the fraction of a hogshead of wine, Ans. $ 10. What part of a hogshead is 9 gallons ? Ans. 1 11. What part of a pound troy is 1002. 10pwt. 10yrs.? Ans. jos DECIMAL FRACTIONS. A Decimal Fraction is that whose denominator is an unit, with a cypher, or cyphers annexed to it, Thus, t'or Tắc: hồ , &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 understol, 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, ' , is written .5; 945; 106,725, &c. But if the numerator las not so many places as thie denominator has cypliers, put so many cyphers before it, viz.. at the left hand, as will make up the defect; su write too thus, ,11,5 ; and 10 mo thos, ,006, &c. Nore. The point prefixell is called the separatrix. Decimals are counted from the left towards the right harid, and each figure takes its value by its distance fro:n 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. Cyphers placed at the right hand of a decimal fraction dlo not alter its value, since every significant figure con. timies to possess the saine place: $0,5 „50 and 9509 are all the saine valur, and equal to is or lo But cypers placed at the left hand of decimals, le. crease their value in a tentold proportion, by removing ilien fuit:er frien tiigilecimal point. Thus, 15 .05 .005, &c. are five terith parts, five hundredth parts, five tlouwandth parts, dic. 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 in. stance, a fraction beginning with any figure less than ,9 such as ,899299, dic. il extended to an infinite number af figures, will not equal ,9. ADDITION OF DECIMALS. RUI.P. 1. Place the numbers, wnether mixed or pure decimals, under each other, according to the value of their places. 2. Find their sum as in whole numbers, and perint off 801 many places for the decimals, ils are equal 2o the great. cat number suf decimal parts in any of the given numbers. EXAMPLES. 41,653 $6,05 Thus, 4.6109 Sum, 109,512 which is 103 integers, and the parts of an unit. Or, it is 103 units, and 3 lenth parts, i hune drrelih part, ani 2 thousandth parts of an unit, or 1. llence we may observe, that decimals, and FEDERAL Mosty, are subject to ride, and the same law of autatiua, and consequently of operation. for since. dollar is the money unit; and a dime being the tenth, a cent the hundredth, and a mill the thousandth part of a dollar, or unit, it is evident that ang mmber of dollars, dimes, cells and mills, is simply the expression of dollars, and doesmai parts of a colar: 'Iius, 11 dollar'n, û dimes, 5 cent», li,tij ar 110 dul. &c. . Add the following mirea numbers together (3) mars, 48,9109 1.8191 3,1030 :012 5. Add the following sume of Dollars logether, viz.. 81:9.54563 7.951 +2.16-18. torinoli Hors. 856,5:::5, or 850i, ádi. :'1*. : Homiils. 6. Add the following paarik ost an acre together, sir.. ,: 369+,25 +,634 +,199 tris. 1,8599 arres. 7. Add 72,5+32,071 +2,1574 +3:1,4+2,: 5 Ins. 480,8784 8. Adi 30,07 +200,71 +59,4+3207,1 .Ans. 3497,28 9. Add 71,463 +27,94+16,084+98,009+86.5 Ans. 300 10. Add ,509+,0074+,69+,8408+,6109 Ans. 2,9 11. Add ,67.099+,37+,905 +.026 ใ ins. 2 12. To 9,999999 add one milliouth part of an unit, and the sum wili bé 10. 13. Find thie suin of 'I'wenty-five hundreditlis, Three hundred and sixty-five thousandths, Six tenths, and jue milliouths, Answer, 1,2LS000 SUBTRACTION OF DECIMALS. RULE. Place the numbers according to their value ; then sub tract as in whole numbers, and point off the decimals as in Addition. 6. From 480 take 245,0075 Ans. 234.9925 7. From 236 viwis. take 1549 dols. Ans. 825.4.11 8. From ,145 tahe ,09687 Ars, 01816 9. Fron .2754 take ,2371 Ans. ,0383 10. From 271 take 215.7 Anes. 55 11. Froiu 2711,2 take 75,4075 Ans. 194,7925 12. From 107 take ,0007 Ans. 106,9993 13. From an unit, or 1, subtract the millionth part of -tself. us. ,999999 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 prosluct as there are decimal places in both the factors; and if there be IKOt, so many places in the product, supply the defect by prefixing cyphers to the lett hand. |