Subtract .753 from 18. (Note that the point or period is placed to the left of “753” indicating decimals, but in connection with the number “18,” a dot is placed to the right as a mark of punctuation merely, thus showing that “18” is a whole number.) Now from the whole number “18,” which is the minuend because it is the number to be subtracted from, we are to subtract .753, and it is done in this way: Minuend 18.000 Subtrahend .753 ------ 17.247 The three ciphers are added to the minuend to correspond to the decimal places in the subtrahend. It is not necessary to put the ciphers down, but beginners are apt to get confused if there is nothing there to correspond to the decimals below. Annex as many ciphers to the minuend as there are decimals in the subtrahend, and place in the remainder a decimal point under those of the numbers subtracted. Multiplication of decimals differs somewhat from the previous operations mentioned for the reason that we do not necessarily place the decimal points directly under each other. The right-hand figure of the multiplier usually goes under the right-hand figure of the multiplicand and the problem is then worked out as in multiplying whole numbers. When the product is obtained we point off as many decimal places in it as there are in both the multiplier and the multiplicand. Let us take as an example: Multiply 2.648 by 2.35 Multiplicand 2.648 Multiplier 2.35 ----- 13240 7944 5296 ------- Product 6.22280 It will be seen that there are three decimals in the multiplicand and 2 decimals in the multiplier, hence we point off five decimals in the product. In the operation of division of decimals the decimal point is not considered until the result is obtained. If the number of decimal places in the dividend is less than the number of decimal places in the divisor ciphers must be annexed or added to make up the deficiency, and the decimal point is then suppressed, thus reducing the operation to the division of two whole numbers. If there is no remainder, the quotient is a whole number, if there is a remainder, add a cipher to the right of it and place a decimal point to the right of the quotient obtained, then continue the division as far as desirable by adding ciphers to the right of the successive remainders, for each of which a new decimal will be obtained in the quotient. Divide 460 by .5. .5)460(92 45 -- 10 10 -- 0 Fractions are reduced to decimals by annexing ciphers to the numerator and then dividing by the denominator. For instance--5/8 equals what decimal? 8)5.000(.625 = 5/8 48 -- .20 16 -- .40 40 Lessons by Prof. Jean P. Genthon, C.E., Member Society of Municipal Engineers and Author of “The Assistant Engineer,” “The Chief’s” Text Book on Civil Engineering.