This rule will hold in all cases. 1. When the number of decimals are equal in the divisor and dividend, the quotient will be integers, or whole numbers : for placing the first multiple of the divisor under the dividend, according to the rule. Ex. 1.
Y.45)295.75(35 25.35 4225 4225 The unit's place 5, is found to stand under 9, the place of tens in the divi dend ; so that 3, the first figure of the quotient, must be tens also, and 5, the next figure, units. 2. When the number of decimals in the dividend exceed those in the divisor, as, Ex. 2.
24.3)780.516(32.12 72.9 Where 2, the unit's place of the mul tiple of the divisor, stands under 8, the place of tens of the dividend ; whence 3, the first figure of the quotient, must be tens also ; and 2, the next figure, units ; so that the remaining figures, 12, must be decimals. This is done, more shortly, by making as many figures of the quo tient decimals, as there are more deci mal places in the dividend than in the di visor. 3. When there are not so many decimal places in the dividend, as there are in the divisor, cyphers must be added to the right hand of the dividend, to make them equal : thus, to divide 192.1 by
7.684, as in Ex. 3.
7.684)192.100(25 15.368 38420 38420 oz;== Add two cyphers to make the deci mals equal; and, by the above rule, the quotient 25 will be found to be integers, as 5, the place of units, stands under 9, the place of tens. 4. If after division there are not so many figures in the quo tient as there ought to be decimal parts, supply this defect by prefixing cyphers to the quotient found: thus, in Ex. 4.
957)7.2540(.00758 nearly.
6.699 .5550 4785 .7650 7650 The quotient by division is found to be 758; and, by the above rule, the first figure, 7, ought to stand in the decimal place of thousandths, which it is reade to do by prefixing two cyphers.
Vulgar fractions are reduced "to deci mals of the same value, by dividing the numerator by the denominator.
1 10 3 Thus,— — =-..5 and =- 2 ' :c 4 2 2.000000, &c. 7 7 =.285714, nearly.