To divide Decimals by 10, 100, 1000, &c. only remove the Point as many Places further towards the Left Hand as there are Cyphers in the Divisor. Reduction of Decimals. THIS Rule teaches us (Ift) to reduce or change a Vulgar Fraction into a Decimal of the same Value.(2dly) To find the Value of a Vulgar or Decimal Fraction. -And (3dly) To reduce any Part of Coin, Weight, or Measure, to a Decimal. We will begin with the first, which is, To reduce a Vulgar Fraction into a Decimal of the fame Value. Rule. As the Denominator of the Vulgar Fraction is to its Numerator, so is 10, 100, 1000, &c. (or any other Number, which is intended for a Denominator) to the Numerator of a Decimal Fraction. Example 1. Let of any Thing be given, to be reduced to a Decimal of two Places; viz. to have 100 for its Denominator. As 4:3:: 100 3 4) 300 (.75 28 20 20 .. Here are cut off two Places in the Quotient, because there are 2 Cyphers in the third Number: So that we find, that three Parts in four of any Thing is equal to Seventy-five Parts in a hundred of the fame Thing. In the fame Manner will be found equal to .25. Example 2. What Decimal Fraction is equal to of any Thing? As 94: 15 :: 1000 15 5000 1000 94) 15.000 (.159 the Answer. 94 560 470 900 846 (54) This Decimal of 159 is not exactly equal to the given Vulgar Fraction; but by continuing the Divifion it may be carried to what Exactness we please; though in some Cafes it never can be exact. But in this Example, the Remainder does not amount to more than the Half of one ten thousandth Part of the Whole, which is near enough in common Cafes. (2dly.) To find the Value of a Vulgar or Decimal Fraction. Rule. As the Denominator of the Fraction is to its Numerator, so is the Number of Parts in the Integer (or whole Number) to the Value required. Crample 1. What is the Value of of an Hundred Weight? As 16:7:: 112 Pounds in an Hundred Weight. 7 16) 784 (49 Pounds. 144 ... Example 2. What is the Value of .384 of an Hogshead? 63 Answer 24 Gallons, I Pint, and Parts of a Pint, which is a little more than half one. Note. 5 Note. The Value of a Decimal Fraction may be found more elegantly, by only multiplying the Decimal by the Number of Parts in the Integer; remembering to cut off as many Figures in the Product, as there are Places cut off in the Decimal given. Then multiply those Figures cut off, by the Number of Parts in the next inferior Denomination; and cut off as many Places as before; and so proceed till you have brought it down to the lowest Denomination required. Cramples. What is the Value of .384 of an Hogshead? 63 Gallons in an Hogshead. Here the Answer is the fame as on the other Side; but is discovered in less than Half the Quantity of Figures. What is the Value of .5789 of a Pound Sterling, Answer II Shillings and 6 Pence 3 Farthings, and fome- thing more. |