MATHEMATICS 5 



If a product has not as many figures as the sum of the deci- 

 mal 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 2X2 = 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; 

 that is, .002 X.002 = .000004. 



Division of 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 fewer places 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; if the dividend is a whole 

 number, annex as many ciphers as there are decimal places 

 in the divisor; the quotient in either case will be a whole num- 



25.75 82.5 82.50 7.5 



ber. For example, = 10.3; = = 30; = 3. 



2.5 2.75 2.75 2.5 



Carrying 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 -5- 18.1 to three decimal places 



36.5000 



= = 2.016 +. (The sign + thus placed after a number 



IS. 1 



indicates that the exact result would be more than the one 

 given if the division were carried further; thus, if the division 

 were carried to six figures, the quotient would be 2.01657.) 



Reducing a Decimal to a Common Fractioc. 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 = f$& = f. 



Reducing 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, & = 3.0000 -^16 

 = .1875. 



