EXAMPLE I. Multiply 6.827195 by 83.7945, and retain only 2 decimal places in the product. 2. Multiply 6.827195 by 83.7945 and retain 2 decimal places. 3. Multiply 163.43785 by .0851795 and retain 3 decimal places. 4. Multiply 2.38645 by 8.2175 and retain 4 decimal places. 5. Multiply 128.678 by 38.24 and retain 1 decimal place. 6. Multiply .01546968 by 11.7145984 and retain 4 decimal places. 7. Multiply .58647473 by .0053948 and retain 8 decimal places. DIVISION OF DECIMALS. 1. Divide, as in whole numbers, and point off from the right hand of the quotient as many figures for decimals as the decimal places in the dividend exceed those in the divisor; if there be not so many figures in the quotient, supply the defect by adding ciphers to the left hand*. 2. If there be any remainder, after bringing down all the figures in the dividend, or more decimal places in the divisor than there are in the dividend, ciphers may be added to the dividend, if it be finite, or the repeating figures, if it be a repetend, and the quotient carried to any degree of exactness required. 3. To divide by any number that has ciphers annexed, remove the decimal point in the dividend, as many places to the left hand as there are ciphers on the right of the divisor. 1. The number of decimal places in the divisor and quotient must always be equal in number to those in the dividend. Therefore, if there be the same number of decimal places in the divisor as in the dividend, there will be none in the quotient. 2. If there be more in the dividend, the quotient will have as many as the dividend exceeds the divisor 3. If there be more in the divisor than in the dividend, they must be made equal before dividing, and the quotient will then consist entirely of whole uumbers. 4. The place of the decimal point may also be settled thus: the first figure of the quotient is of the same value with that figure in the dividend which stands over units, in the first product; or, which is the same, the first figure of the quotient is always at the same distance from the decimal point, and on the same side as the figure of the dividend, which stands above the unit place of the first product. In Example I., there are 5 decimal places in the dividend, and only 2 in the divisor; therefore, the 3 right hand figures of the quotient must be pointed off for decimals. In Example II., there are 2 more decimal places, in the divisor, than in the dividend; therefore 2 decimal places are added, to make them equal; and, as this is the case, there will be no decimal places in the quotient, when the dividend is exhausted, the first two figures (16) are, therefore, a whole number; but, to have the quotient more exact, other 4 places are added, and, consequently, the quotient will have as many decimal places. The reason for adding 6's to the dividend is, because this figure is a repetend. Convert the divisor into a vulgar fraction, then multiply the given dividend by the denominator, and divide by the numerator of the fraction. * The divisor, in this method, is converted into a vulgar fraction, by Case I. of Reduction; and in Method II, by Case IV. of Vulgar Fractions. When the multiplier is 9, 99, 999, &c. the easiest method of finding the product, is by Rule III, of Simple Multiplication. EXERCISES. 2. Divide 4974 by 8. 5. Divide 37 by .235. 6. Divide .3 by 1.2. 8. Divide 12.3456 by .0081. 9. Divide 577.375 by 23.851. CASE III. To limit the quotient to any number of decimal places*. RULE. Find what place the first figure ought to occupy; that is, how many places from the decimal point it ought to stand: then consider how many figures the quotient ought to consist of, in order to have the required number of places, and point off as * It often happens that there are many places in the divisor, and but few wanted in the quotient: in such cases, this rule is very con venient. |