6 MATHEMATICS 



INVOLUTION AND EVOLUTION 



SIGNIFICANT FIGURES 



In any number, the figures beginning with the first digit* 

 at the left and ending with the last digit at the right, are called 

 the significant figures of the number. Thus, the number 

 405,800 has the four significant figures 4, 0, 5, 8 and the sig- 

 nificant part of the number is 4058. The number .000090067 

 has five significant figures, 9, 0, 0, 6, and 7, and the significant 

 part is 90067. 



All numbers that differ only in the position of the decimal point 

 have the same significant figures and the same significant part. 

 For example, .002103, 21.03, 21,030, and 210,300 have the same 

 significant figures 2, 1, 0, and 3, and the same significant part 

 2103. 



The integral part of a number is the part to the left of the 

 decimal point. 



SQUARE AND CUBE ROOTS 



By means of the accompanying table, the square, cube, 

 square root, cube root, and reciprocal of any number may be 

 obtained correct always to five significant figures, and in the 

 majority of cases correct to six significant figures. 



If the number whose root is to be found contains fewer 

 than four significant figures, the required 'root can be found 

 in the table, the square root under Vn, or "VlOw, and the cube 

 root under 3ln, ^10n, or 'S'lOOn, according to the number of 

 significant figures in the integral part of the number. Thus, 

 \.;.l 1^1.772; >/31.4= \1(>X:U 1 = r,.C,(r,7; V.'U l = 1.46434; 

 V'.M = ^10><3.14 = 3.15484; %14= ^100 XiU 4 = 0.79688. 



In order to locate the decimal point, the given number must 

 be pointed off into periods of two figures each for square root 

 and three figures each for cube root, beginning always at the 

 decimal point. Thus, for square root: 12703, 1'27'03; 12.703, 

 12.70'30; 220000. 22WOO; .000442, .OO'04'42; and for cube 

 root: 3141.6, 3'141.ti; i7L".Mi428. 67'296'428; .0000000217, 

 .000'000'021'700; etc. 



*If ciphers are used simply to locate the decimal point, thev 

 must not be counted as digits. 



