In decimals, whole numbers are divided into tenths, hundredths, etc.; thus, 1/10 is written .1; .08 is read 8/100, the value the number being indicated by the position of the decimal point; that is, one figure after the decimal point is read as so many tenths; two figures as so many hundredths; etc. Moving the decimal point to the right multiplies the number by 10 for every place the point is moved; moving it to the left divides the number by 10 for every place the point is moved. Thus, in 125.78 (read 125 and 78/100), if the decimal point is moved one place to the right, the result is 1,257.8, which is 10 times the first number; or, if the point is moved to the left one place, the result is 12.578 which is 1/10 the first number, moving the point being equivalent to dividing 125.78by 10.

Annexing a cipher to the right of a decimal does not change its value; but each cipher inserted between the deci-mal point and the decimal divides the decimal by 10; thus, in 125.078, the decimal part is X of .78.

To add decimals. Place the numbers so that the decimal points are in a vertical line, and add in the ordinary way, placing the decimal point of the sum under the other points.

To subtract decimals. Place the number to be subtracted with its decimal point under that of the other number, and subtract in the ordinary way.

 101.257 12. 43.006 920.600 1,077.827 917 482.710 434.968

To multiply decimals. Multiply in the ordinary way, and point off from the right of the result as many figures as there are figures to the right of the decimal points in both numbers multiplied; thus, in the example here given, there are three figures to the right of the points, and that many are pointed off in the result. If either number contains no decimal, point off as many places as are in the number that does.

If a result has not as many figures as the sum of the decimal places in the numbers multiplied, prefix enough ciphers before the figures to make up the required number of places, and place the decimal point before the ciphers. Thus, in .002 X .002, the product of 2 X 2 = 4; but there are three places in each number; hence, the product must have six places, and five ciphers must be prefixed to the 4, which gives .000004.

To divide decimals. Divide in the usual way. If the dividend has more decimal places than the divisor, point off, from the right of the quotient, the number of places in excess. If it has less than the divisor, annex as many ciphers to the decimal as are necessary to give the dividend as many places as there are in the divisor; the quotient will then have no decimal places. For example, 25.75/2.5=10.3; 82.5/2.75=

82.5/2.75=30; 7.5/2.5=3.

To carry a division to any number of decimal places.

Annex ciphers to the dividend, and divide, until the desired number of figures in the quotient is reached, which are pointed off as above shown. Thus, 36.5/18.1 to three decimal places = 36.5000/18.1=2.016+. (The sign+ thus placed after a number indicates that the exact result would be more than the one given if the division were carried further.)

To reduce a decimal to a common fraction. Place the decimal as the numerator; and for the denominator put 1 with as many ciphers as there are figures to the right of the decimal point; thus, .375 has three figures to the right of the point; hence, .375 in.=375/1000=3/8 in.

 21.72 34.1 2172 8688 6516 740.652

To reduce a common fraction to a decimal. Divide the numerator by the denominator, and point off as many places as there have been ciphers annexed; thus, 3/16 in.=3.0000/16 = .1875 in.