Numerator 7 The Numerator, in the Vulgar Form, is always wrote over the Denominator, and these are separated by a small Line, thus - or f's Denominator the first of these is called 5 Twelfths, and the latter 7 Twelfths of an Inch, Yard, Perch, &c. or of whatever the whole Thing originally was. Fractions are expressed in two Forms, that is, either vulgarly or decimally. All Fractions whose Denominators do not consist of a Cypher or Cyphers fet after Unity, are called vulgar ones, and their Denominators are always wrote under their Numerators. The treating of these would be foreign to our present Purpose. But Fractions whole Denominators consist of an Unit, prefixed to one or more Cyphers, are called Decimal Fractions ; the Numerators of which are wrote without their Denominators, and are distinguished from Integers by a Point prefixed : Thus i 3름 142 and 1785 in the Decimal Form, are expressed by .2.42 .172. The Denominators of such Fractions always consisting of an Unit, prefixed to as many Cyphers as there are Places of Figures in the Numerators, it follows, that any Number of Cyphers put after those Numerators, will neither increase or lessen their Value: For 13 and are all of the same Value, and will stand in the Decimal Form thus .3 .30 .300 ; but a Cypher or Cyhphers prefixed to those Numerators, lessen their Value in a tenfold Proportion : For and to which in the Decimal Form we denote by :3.03 and .003, are Fractions, of which - the first is ten Times greater than the second ; and the second, ten Times greater than the third. Hence it appears, that as the Value and Denomination of any Figure or Number of Figures in common Arithmetic is enlarged, and becomes ten 100 72 IOC 3 оо 3 003 1000 or or a hundred, or a thousand Times greater, by placing one, or two, or three Cyphers after it; fo in decimal Arithmetic, the Value of any Figure or Number of Figures, decreases, and becomes ten, or a hundred, or a thousand Times less, while the Denomination of it increases, and becomes so many Times greater, by prefixing one, or two, or three Cyphers to it : And that any Number of Cyphers, before an Integer, or after a decimal Fraction, have ņo Effect in changing their Values. Integers. Decimals. I 2 7 1 6 3 5 I 2 3 6 7 Tens Units Hundreds Thousands Tenths er Addition of DECIMAL S. Having placed those Figures which are equidistant from the Point, (as well Integers as Fractions) under each other, add them as if they were Integers. EX A M P L E S. Add 4.7832 3.2543 7.8251 6.03 2.857 and 3.251 together. Place them thus, 4.7832 3.2543 7.8251 6.03 2.857 3.251 Answer 28.0006 B 2 Add Add 6.2 121.306 .75 2.7 and .0007 tow gether 121.306 .75 2.7 .0007 Answer 130.9567 What is the Sum of 6.57 1.026 -75 146.5 8.7 526 3.97, and .0271? Aniwer 693.5431. What is the Sum of 4.51 146.071 .507 .0006 132 62.71 507 7.9 and 10712? Answer 354.31272. Subtraction of DECIMALS. Having placed the Figures which are equi-distant from the Point, under each other ; deduct as if they were Integers. From 84 take 82.3412 Answer 1.6588 Multiplication of DECIMAL S. Place the Multiplicand, and Multiplier, after any Manner under each other; and having multiplied as in whole Numbers, cut off as many Places of Decimals in the Product, counting from the right Hand towards the left, as there are in the Multiplicand, and Multiplier : But if there be not a fufficient Number of Places in the Product the Defect may be supplied, by prefixing Cyphers thereto. For the Denominator of the Product, being an Unit, prefixed to as many Cyphers, as the Denominators of the Multiplier and Multiplicand contain of Cyphers, it follows, that the Places of Decimals in the Product, will be as many as in the Numbers from whence it arose. Multiply 121.6 by 2.76 2.76 7296 8512 2432 Answer 335.616 Multiply .0089789 by 1085 Answer 9.7421065 Answer .0337939940 1 Devision of DECIMALS, Having divided as in whole Numbers, annexing Cyphers to the Dividend if they be wanted; the Decimal Places in the Divisor and Quotient must be equal to those in the Dividend, and the Defect supplied by prefixing Cyphers to the Quotient. For the Dividend is a Product contained under the Divisor and Quotient; and that Product contains as many Places of Decimals as the Numbers do from whence it arose : Therefore the Difference between the Number of Decimals in the Dividend and Divifor, must be cut off in the Quotient. EX A M P L E S. .12). 144(1.2 24 |