(3dly.) Some Part of an Integer being given, to find (nearly) what Decimal it is of the Integer:-or, to reduce any Parts of Money, Weights, and Measures, to a Decimal equal to it. Rule. First, make it a Vulgar Fraction by writing the Number of the same Parts contained in the Integer under it; then reduce that Fraction to a Decimal as before. Examples. What Decimal of a Foot is 3 Inches? In a Foot are 12 Inches, consequently the Vulgar Fraction is 3 Then, as 12::3:: 100 3 12) 300 (.25 24 60 60 Let it be required to reduce 125. 2d. to the Decimal of a Pound Sterling. In 125. 2d. are 146 Pence; and in a Pound are 240 Pence; 146 therefore the Vulgar Fraction is 48. 240 Then, as 240 : 146 :: 1000 1000 240) 146000 (.608 Answer. 1440 2000 1920 (80) What Decimal of an Hundred Weight is 71 lb.? In an Hundred Weight are 112 lb. therefore the Vulgar Fraction is What Decimal of a Pound Avoirdupoise is 11 Ounces? In one Pound Avoirdupoise is 16 Ounces: the Vulgar Fraction, therefore, is ; then say, As 16:11:: 1000 11 1000 1000 16) 11000 (.687 Answer. 96 140 120 112 (8) In like Manner the Decimal of 34 Inches will be found to be .2708 of a Foot. For as 48, the Quarters of Inches in a Foot, is to 13, the Quarters of Inches in 34 Inches; fo is 1000 to .2708, the Decimal required. The Vulgar Fraction being of a Foot. An An Expeditious Method of discovering the Value af a Decimal of a Pound Sterling. Rule. Double the Figure which stands next the Point in the Decimals for fo many Shillings; and if the next Figure be 5, or more, add 1 to the former Shillings; and for what it is under or above 5, reckon so many Tens, which added to the Figure in the third Place, will be fo many Farthings, abating I for every 24; which brought into Pence, and added to the Shillings before found, will give the true Value of the Decimal required. An Example or two will make all plain. What is the Value of .782 of a Pound Sterling? Answer 155. 72d. Here, the first Figure 7 being doubled is 14; the second being 8, reckon I more for 5, which makes 15 Shillings; the remaining 3 above 5 added as fo many Tens to the 2 in the third Place is 32; which lessened by 1, because more than 24, makes 31 Farthings, or 7 d. this added to the 15 Shillings, gives the Answer as above. What is the Value of .5789 of a Pound Sterling? Where the Decimal consists of four Figures, the last may be wholly omitted as inconfiderable. What relates to the Doctrine of Repetends or circulatin Decimals, with Contractions in Multiplication and Divisio as being not absolutely necessary here, will be reserved fo a. Place in a future Work. The The Rule of Three in Decimals. THIS Rule is performed the same way as in nole Numbers, regard being had to cutting off the Decials right in the Multiplications and Divisions; as in the lowing Examples. Example 1. ppose Yard of Cloth cost 17s. 6d. what will 47 Yards cost? Answer 668.5 Shillings, which reduced into Pounds by viding by 20, is 33.425; or 331. 8s. 6d. |