MULTIPLICATION OF DECIMALS BY THE What is the product of 1246.329 and 1.435 to two decimal There being three decimal places in each factor, if we multiply in the usual manner we shall have to point off six places in the product. That is, in order to get the two decimal figures we want, we get four more that we don't want. If, in order to save figures, we should strike off the 5 thousandths of the multiplier, there would be an error of over 6 in the product obtained. If we should drop the 9 thousandths of the multiplicand, there would be an error of .01. The best we can do in this sort of way is to call the multiplicand 1246.33, and retain the multiplier as it is. But this saves only four figures, and we have had to go through a preliminary calculation, though in this particular case it is a very simple one, in order to find out what to do. Hundredths by units produces hundredths; tenths by tenths, hundredths; units by hundredths, hundredths; tens by thousandths, hundredths. So, if we write the units of the multiplier under the hundredths of the multiplicand, and the remaining digits of the multiplier reversed, that is, 4, 3, 5 to the left instead of to the right, and in multiplying, commence each time with the digit of the multiplicand directly over the one of the multiplier we are then using, disregarding the lower denominations of the multiplicand, with the exception of adding in what there is to carry from the next lower denomination, each partial product will be in hundredths, and the sum of the partial products thus obtained will be correct to two decimal places. What is the product of .23047651 and 35.12043 to three decimal places? .23047651 2153 6914 1152 23 5 8.094 Write the units of the multiplier under thousandths of the multiplicand, and the rest of the multiplier reversed. To be sure of the last figure of the product, it may sometimes be well to go one decimal place further than the last one really wanted, and then omit the last figure obtained. But if we look out sharply for what there is to carry, we shall usually be exactly right without taking this precaution. 216. Multiply 12.491 by .36 to two decimal places. .17653 by 122.5 to one decimal place. 60.31654224 by 521.2 to four decimal places. 340.6582716354 by 3.7012407853612 to three decimal places. .1243 by 3.256 to the nearest thousandth. 1243. by 325.6 to the nearest thousand. 33546.86 by 5728.6 to the nearest million, CONTRACTED DIVISION OF DECIMALS. The same principle may be applied to the division of decimals. Divide 1897.5431 by 32.467 to three decimal places. We first find how many figures there will be in the quotient. 32 will not go in 18, but will go in 189; so the first figure of the quotient will be tens, and the total number of figures, five. As soon as the number of figures of the quotient remaining to be found is one less than the number in the divisor, we stop bringing down from the dividend, and drop the last figure of the divisor before each partial division. In multiplying, we add what there is to carry from the multiplication of the digit last dropped. To be sure of the last digit of the quotient, it may sometimes be well to delay the contraction until the number of figures of the quotient remaining to be found is two less than the number in the divisor. Divide 1764 by 3681 to two decimal places. 3681) 1764 (.48 29 217. Divide 286 by 13.47 to two decimal places. 132674 by 9321765 to three decimal places METHODS OF CALCULATING INTEREST. Reverse multiplication is especially applicable to figuring interest. What is the amount of $1642.27 for 2 yrs. 3 mos. 16 dys. at 6%? What is the interest on $1642.27 from July 26 to Dec. 19 at 6%? 1642.27 532 3285 492 82 55 It is easy to see where the first figure of the multiplier should be placed. Unless we want the result to mills, units of the multiplier go under hun(=+) dredths of the multiplicand; hundredths, two places beyond. |